Congressional Republicans are collecting evidence to show an extensive, election year, anti-Trump conspiracy between Hillary Clinton operatives such as Fusion GPS and Barack Obama appointees at the Justice Department and the FBI.

The investigation took a new turn last week. Fusion co-founder Glenn Simpson decided to invoke the Fifth Amendment rather than testify under subpoena before a special House Republican task force.

The Republicans see Mr. Simpson as the key middleman between Justice and the Clinton campaign. He orchestrated the Democrat-financed dossier on which the FBI built its early investigation of candidate Donald Trump. Republicans believe the unproven dossier, with its charge of extensive Trump-Russia collusion, is a sham perpetrated by Democrats and the press.

“Glenn Simpson was an absolutely essential figure in launching the entire Russia collusion hoax,” a Republican congressional staffer told The Washington Times.

Mr. Simpson decided to invoke his Fifth Amendment rights during the same week that Deputy Attorney General Rod Rosenstein balked at testifying. Republicans want information about his May 2017 meeting with then-FBI Deputy Director Andrew McCabe. He said in a memo that Mr. Rosenstein talked of secretly recording the president, The New York Times reported.

“You know we’re getting close when first Rosenstein is a no-show, and now Glenn Simpson is taking the 5th,” tweeted Rep. Jim Jordan, Ohio Republican.

Mr. Simpson testified to two congressional committees last year and then urged the release of transcripts.

But his attorney, Joshua A. Levy, informed the House task force last week that he would defy a subpoena. Mr. Levy hasn’t responded to attempts by The Times to obtain a comment.

Mr. Levy sent an Oct. 11 letter to House Republicans blasting their investigation.

“This Committee’s inquiry is not designed to discover the truth,” Mr. Levy said. “The obvious — and at times explicitly stated — goal of this Committee is to discredit and otherwise damage witnesses to Russia’s interference in the 2016 election, all as part of an effort to protect a President who has sought to placate and curry favor with a hostile foreign power and who demands that the Justice Department stop investigating him.”

What has changed?

As they dig deeper and talk to Obama people who worked with Mr. Simpson, Republicans believe some of his congressional testimony hasn’t been truthful.

For years Mr. Simpson and Fusion’s other former Wall Street Journal journalists have worked in secret to hand out juicy tidbits to news bureaus — as long as no company DNA is left behind.

But the unverified dossier disrupted their business model.

The Fusion GPS exposure started in 2017 when Rep. Devin Nunes, California Republican, unleashed his subpoena powers. He forced Democrats to acknowledge that the crown jewel of Fusion’s research — the dossier — was funded by the Democratic National Committee and the Hillary Clinton campaign.

For the first time, the public learned that former British spy Christopher Steele’s dossier, with its tales of Trump-Russia conspiracies that remain unconfirmed, wasn’t an intelligence report. It was opposition research that used Democratic money to tap a host of unknown Kremlin agents as sources.

Mr. Nunes, chairman of the House Permanent Select Committee on Intelligence, then disclosed that the FBI embraced that very same piece of Democratic research to obtain court-authorized wiretaps on a Trump volunteer.

The conspiracy grew larger this year. The task force of the House Judiciary and Oversight and Government Reform committees began summoning the FBI and Justice Department hierarchy for closed-door questioning.

Those filing in: Peter Strzok, the fired FBI agent who vowed to stop Mr. Trump; his lover, Lisa Page, a former FBI counsel; James Baker, the FBI’s former general counsel; and Bruce Ohr, an associate deputy attorney general. All have been fired, forced to resign or transferred.

In October 2016, the FBI fired Mr. Steele. He violated his agreement with the bureau by leaking to leftist Mother Jones magazine. The FBI didn’t know it at the time, but Mr. Steele already had broken the rules repeatedly by briefing many of Washington’s mainstream media at Mr. Simpson’s request.

Mr. Steele, an avowed enemy of Mr. Trump‘s, kept talking to the FBI through a cutout, Mr. Ohr. Mr. Steele relayed dossier material to the No. 4-ranked Justice lawyer, who then provided the anti-Trump material to the investigation leader, Mr. Strzok. Mr. Ohr’s wife, Nellie, a Russia scholar, worked for Mr. Simpson at Fusion as a Trump-Russia researcher. Mr. Simpson also talked to Mr. Ohr.

There was another channel.

The Hill newspaper reported that the FBI’s Mr. Baker spoke during the election campaign with at least one lawyer from Perkins Coie, the firm representing the Democratic National Committee. The Hill said attorney Michael Sussman provided a thumb drive on alleged Trump-Russian collusion — a phenomenon much talked about but still unproven publicly.

Perkins Coie was the conduit for at least $160,000 in Clinton and Democratic payments to Mr. Steele.

The Baker-Sussman connection is additional evidence that the FBI was fully aware that the dossier on which it relied was paid opposition research.

Questions of veracity

The House intelligence committee’s majority Republican final report stated that “the political origins of the Steele dossier were then known to senior DoJ and FBI officials” in October 2016. That was when agents used it to secure a court-approved wiretap on a Trump volunteer. Justice invoked the dossier three more times for a year’s worth of wiretaps and never told the approving judge that it was Democratic Party research on Mr. Trump.

Now, Republicans are questioning Mr. Simpson’s veracity. Some examples:

• He told the Senate Judiciary Committee that he had no anti-Trump clients after the election.

But Republicans unearthed a 2017 FBI interview report with Daniel Jones, a former staffer of Sen. Dianne Feinstein, California Democrat. Mr. Jones runs an opposition research firm called Penn Quarter. He told the FBI that he raised $50 million from wealthy donors to investigate Mr. Trump. One of the firms he hired, he said, was Fusion GPS. He said he also hired dossier writer Mr. Steele.

If Mr. Jones is accurate, then Mr. Simpson did have an anti-Trump client after the election.

• Mr. Simpson told the same committee last year that he reached no conclusions on a shaky accusation that the Trump campaign maintained a direct link to Russia’s Kremlin-linked Alfa Bank via a dedicated computer server.

Cyberspace specialists say the server wasn’t for Russia. The server address placed it near Philadelphia as a conduit for spam hotel marketing, not Russia collusion.

The Washington Times reported that Mr. Ohr’s notes show that Mr. Simpson did in fact have an opinion on the server and tried to sell it to Justice. Mr. Simpson told him in 2016 that the server was indeed used for Trump-Russia communication and wasn’t spam.

• The Daily Caller reported that Mr. Simpson told Mr. Ohr that a Washington lawyer had warned the National Rifle Association about illegal Russian donations to its political action committee.

The lawyer, Cleta Mitchell, says she never made such a statement and has not worked for the NRA in years. Ms. Mitchell, who practices political law and has represented Republican election committees, said Mr. Simpson violated federal law by providing the Justice Department with bogus information.

She told The Daily Caller that she had wondered who gave the allegations to McClatchy news service, which reported her supposed NRA warning and her denial. Now she knows it was likely Glenn Simpson.

McClatchy also reported that the government has evidence that former Trump attorney Michael Cohen traveled to Prague during the election to meet with Russian President Vladimir Putin’s staff. Mr. Simpson has pushed that story, which came from the Steele dossier.

No confirming evidence has emerged about such a trip. Cohen, now a convicted tax cheat and estranged from Mr. Trump, continues to deny that he ever went to Prague.

• Mr. Simpson testified under oath that he first spoke to Mr. Ohr after the election, around Thanksgiving 2016. His goal was to make sure the Obama Justice Department knew of Mr. Steele’s allegations against President-elect Trump.

“During the election, no,” Mr. Simpson said when asked whether he had heard from anyone in Justice or the FBI.

But congressional investigations now know from Mr. Ohr’s notes that he and Mr. Simpson were talking during the election. Mr. Ohr was a conduit to Mr. Strzok.

• Mr. Simpson also told the Senate Judiciary Committee that he employed only one Russian speaker, a contractor.

Committee staffers asked whether he received “any other support from Russian-speaking individuals in reviewing the Russian documents.”

“Not in my company, at least not that I can recall,” he answered.

But he employed a second Russian speaker, Mr. Ohr’s wife, Nellie. The fact emerged three months after Mr. Simpson’s testimony in bank records subpoenaed by Mr. Nunes. Republicans contend Mr. Simpson was trying to hide her Fusion connection.

Democratic reset?

“It’s not surprising he’d plead the Fifth rather than testify under oath to Congress again,” the Republican staffer told The Times.

Mr. Ohr appeared before the House joint task force in August, after which Mr. Trump sent out one of several tweets attacking him: “Wow, Nellie Ohr, Bruce Ohr’s wife, is a Russia expert who is fluent in Russian. She worked for Fusion GPS where she was paid a lot. Collusion! Bruce was a boss at the Department of Justice and is, unbelievably, still there!”

An example of how the Steele dossier greatly influenced the FBI is contained in a New York Times story. In September 2016, the FBI questioned Russian oligarch Oleg Deripaska on his knowledge of former Trump campaign manager Paul Manafort working with the Kremlin on election interference.

Mr. Ohr and Mr. Steele had been working secretly to turn Mr. Deripaska into an informant.

Where did the FBI receive the allegations about Manafort?

After Russia’s stolen Democratic Party emails showed up publicly on WikiLeaks, Mr. Steele wrote a dossier memo that July 2016 saying Manafort and Trump campaign volunteer Carter Page worked together with the Kremlin.

There is no public evidence of that assertion. Manafort’s defense attorney filed a motion in court that quoted special counsel Robert Mueller as saying no evidence of Manafort-Russia government communications existed. Mr. Page, the FBI wiretap target, has said the charge is fiction.

The Republican task force is on the clock. If Democrats gain control of the House in the midterm elections, then Rep. Adam B. Schiff would take charge of the House intelligence committee.

The California Democrat has enthusiastically supported Mr. Steele and his Democrat-financed dossier while dismissing all of Mr. Nunes‘ disclosures on how the FBI relied on it.

The Nunes and joint task force investigations will surely come to an end, replaced by reopening the Trump-Russian collusion inquiry, which Mr. Nunes‘ majority concluded didn’t exist.

Mr. Schiff has said he would open an investigation into suspected Trump money-laundering. He also might look at the NRA, a prime Republican donor, for illegal Russian influence.

In a Sept. 28 tweet, Mr. Schiff criticized Mr. Nunes for the decision to seek declassification of witness transcripts.

“House Intel GOP stonewalled the release of witness interviews until the last day,” he said. “And hiding behind closed doors, they rejected the disclosure of key testimony. … They call this ‘transparency.’”

Mr. Schiff mentioned former CIA Director John O. Brennan and former FBI Director James B. Comey as two of the witnesses “rejected” by the majority.

Democrats leaked a number of stories during committee’s Russia investigation. None quoted Mr. Brennan or Mr. Comey on evidence of collusion.