At the heart of the allegations of collusion between Donald Trump's presidential campaign and the Russian government are a Maltese professor who has gone quiet and an apparently defunct London academy with no forwarding address.

The guilty plea entered by Mr. Trump's one-time foreign affairs adviser George Papadopoulos – who admitted to charges of making false statements to the FBI about his campaign-time contacts with Russian officials – sent shockwaves through the U.S. political establishment after it was published on Monday. It's now believed that Mr. Papadopoulos, the first person convicted in a wide-ranging probe into alleged Russian interference in the 2016 U.S. presidential election, has been co-operating for months with the investigation headed by special counsel Robert Mueller.

Mr. Trump's one-time campaign director, Paul Manafort, and his associate Rick Gates, were separately indicted on Monday on charges relating to their work for Ukraine's former Moscow-backed president, Viktor Yanukovych.

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The evidence made public as part of Mr. Papadopoulos's plea bargain created a new mystery: Who was the man, referred to only as "The Professor" in the court documents – a "citizen of a country in the Mediterranean" and a "professor of diplomacy based in London" – who put Mr. Papadopoulos in contact with his friends in Moscow?

It took journalists a few hours on Monday to identify "The Professor" as Joseph Mifsud, a Malta native who was the director of an obscure institution called the London Academy of Diplomacy. But by the time Mr. Mifsud's name was publicly linked to Mr. Papadopoulos's, the professor's mobile phone was switched off, with an answering machine picking up after a single ring.

(Before apparently switching off his phone, Mr. Mifsud spoke to The Daily Beast news website long enough to confirm that he knew Mr. Papadopoulos, while dismissing the allegations contained in the U.S. District Court filing as "a laughing matter.")

On Tuesday, there were almost no trace of "The Professor," or the London Academy of Diplomacy. While the academy once shared office space with three other educational institutes in a five-floor building in London's Aldgate district, the receptionist at the building said on Tuesday that the London Academy of Diplomacy had moved out six months earlier. "I honestly don't know where they are now," she said. The academy's London phone number appeared to have been disconnected before Monday.

Prof. Mifsud was equally hard to find. His Facebook page that existed Monday night – showing a network of friends around the world that included Mr. Papadopoulos as well as several low-level Russian officials – was deleted overnight, as was his professional page at the London Centre of International Law Practice, another unheralded institution that until Monday claimed Prof. Mifsud as its "Director: International Strategic Development."

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Prof. Mifsud told an interviewer several years ago that the London Academy of Diplomacy taught diplomatic skills – everything from how to dress for a diplomatic function to how to advance your country's interests using social media – to "people who would like to work in areas adjacent to diplomacy," such as businessmen or staff at non-government organizations.

The article, printed in The Times of London, gave no information about how many people worked or studied at Prof. Mifsud's academy. Nor did it mention any prominent alumni. Carla Figueira, a lecturer on international cultural diplomacy at the University of London, said that in her field "the London Academy of Diplomacy is not known at all."

What Prof. Mifsud was known for – according to the agreed statement of facts in the case against Mr. Papadopoulos – was providing a back-channel way of communicating with Moscow. One of the most recent photographs of Prof. Mifsud available online shows him standing with Ernest Chernukhin, a diplomat at the Russian Embassy in London, who visited the London Academy of Diplomacy in July of this year.

The U.S. court documents state that it was "The Professor" who put Mr. Papadopoulos in contact with two other individuals, named only as "The Female Russian National" and the "Russian MFA [Ministry of Foreign Affairs] Connection." (The "Female Russian National" is originally introduced to Mr. Papadopoulos as the niece of Vladimir Putin, though it is later established that she was not a relative of the Russian President.)

It's also The Professor who initially told Mr. Papadopoulos – and thus the Trump campaign – that Russia had obtained information that could damage Mr. Trump's rival for the presidency, Democratic candidate Hillary Clinton.

"They [the Russians] have dirt on her … they have thousands of e-mails," Mr. Papadopoulos told the Federal Bureau of Investigation earlier this year, describing what The Professor had told him.

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"Following the conversation, defendant Papadopoulos continued to correspond with Campaign officials, and continued to communicate with the Professor and the Russian MFA Connection, in an effort to arrange a meeting between the Campaign and the Russian government," the agreed statement of facts reads.

The court document suggests Prof. Mifsud heard about the Clinton e-mails while attending an April, 2016, meeting of the Valdai Club, a Kremlin-sponsored discussion forum that brings together Russian officials and foreign international relations experts.

While few in London knew of Prof. Mifsud or his London Academy of Diplomacy before Monday, the Valdai Club made him a featured speaker at its April, 2016, conference in Moscow on global energy development.

Piotr Dutkiewicz, the director of the Centre for Governance and Public Management at Carleton University in Ottawa – and a regular Valdai Club participant – said he had never met or heard of Prof. Mifsud, nor seen him at any of the larger Valdai Club meetings that were personally attended by Mr. Putin.

Prof. Dutkiewicz questioned whether the Kremlin would use Prof. Mifsud – whom he called a "completely peripheral figure" – for something as sensitive as reaching out to a U.S. presidential candidate.

But Prof. Mifsud appears to have worked hard to ingratiate himself to the Russian government. Before this week, much of his public work involved speaking to Kremlin-controlled media outlets or cheerleading for Kremlin-allied regimes in the former Soviet Union.

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In 2013, Prof. Mifsud was quoted by Azerbaijan's state-run news service praising the "great changes" that President Ilham Aliyev had "made on behalf of the common people" in his country.

Two years later, he was in the news in Kazakhstan, lending a foreign voice of approval to the way the country's presidential elections were run. "I can confidently say that the election campaign in Kazakhstan met all [European Union] standards. It was like a holiday for people. I saw it in many electoral districts," Prof. Mifsud told the country's official wire service.

President Nursultan Nazarbayev, a close ally of Mr. Putin who has ruled Kazakhstan since 1989, won the 2015 election with 97.7 per cent of the vote.

Prof. Mifsud was also a harsh critic of the Western-led sanctions against Mr. Putin's inner circle that were applied following Russia's move to seize and annex the Crimean Peninsula in 2014. The idea of dropping sanctions against Russia – and possibly recognizing the annexation of Crimea – was an idea Mr. Trump himself would flirt with throughout his successful run to the White House.

"I don't think that the U.S. has the energy to continue with this," Prof. Mifsud told the Kremlin-run Sputnik service late in 2014, referring to the tit-for-tat sanctions war. "The global security and economy needs partners and who is better in this than the Russian Federation?"