A photograph of Joseph R. Biden on a golf outing with his son Hunter and his son’s business partner in a Ukraine venture has cast doubts upon the former vice president’s claim that his family never discussed their business deals.

The claim is Mr. Biden’s chief pushback against allegations that as vice president he intervened in Kyiv to block a 2016 corruption probe of Ukraine natural gas company Burisma Holdings where Hunter Biden had a job on the board of directors.

“I’ve never spoken to my son about his overseas business dealings,” Mr. Biden told reporters last month on the campaign trail in Iowa.

The corruption charge also is at the heart of the House Democrats’ impeachment inquiry regarding President Trump’s July 25 phone call in which he pressured the Ukraine president to open an investigation of the Bidens’ activities in the country.

The 2014 photograph shows a golf foursome that includes Mr. Biden, Hunter Biden and Devon Archer, a colleague of Hunter Biden who also served on the board at Burisma.

That was the same year the elder Mr. Biden became the Obama administration’s point man in Ukraine and Hunter Biden and Mr. Archer scored high-paying gigs at Burisma.

Hunter Biden, a Yale-educated lawyer with no experience in the energy industry, was paid $50,000 a month.

The photograph did not confirm that Mr. Biden and his son discussed Burisma or any other of the business deals involving Hunter Biden and Mr. Archer. But it did highlight the close relationship of the three men at the time of the Ukraine deal and raise questions about what they discussed.

The Biden campaign refused to comment on the photograph.

The allegations of corruption Mr. Trump has leveled against Mr. Biden are similar to those House Democrats are pursuing against Mr. Trump in an impeachment inquiry. Both involve abuse of political power for personal gain.

Mr. Trump is accused of prodding the Ukrainian president to investigate a political rival. Mr. Biden is accused of prodding Kyiv to stop an investigation involving his son’s employer.

During a 2016 visit as vice president to Kyiv, Mr. Biden threatened to withhold $1 billion in U.S. loan guarantees if the country’s leaders did not fire Ukraine’s top prosecutor, Yuri Lutsenko, who was accused of not doing enough to fight rampant corruption.

At the time, Mr. Lutsenko’s office also was investigating money laundering and fraud at Burisma.

Mr. Trump and his allies have seized on the photo, which was first reported by Fox News, as evidence that Mr. Biden knows more than he lets on about his son’s sweetheart deals in Ukraine and business ventures around the globe that appeared to cash in on his father’s political clout.

Mr. Trump posted a video on Twitter that featured a clip of Mr. Biden saying, “I’ve never spoken to my son about his overseas business dealings.” The video then cuts to a popular meme of the music video for the 2005 Nickelback single “Photograph,” with the golf photo inserted in the starring role.

In the original video, vocalist Chad Kroeger holds up a framed photographed and sings:

“Look at this photograph / Every time I do it makes me laugh / How did our eyes get so red? / And what the hell is on Joey’s head?”

The meme involves people digitally inserting other photographs into the frame.

Mr. Trump’s version inserted the golf photo with the words “Ukraine gas exec” superimposed on Mr. Archer and Mr. Biden and his son labeled with their names.

The outlines of red hearts are then drawn around the faces of the three men in the photo.

Twitter removed the video within 12 hours, citing a complaint by Nickleback that it infringed on the copyright.

Mr. Trump’s private lawyer, former New York Mayor Rudolph W. Giuliani, later tweeted the same video.

“If this is true, that Biden didn’t know about his son’s overseas business dealings, then where else was the son doing business that was in conflict with the best interest of the United States? Russia, Venezuela, Cuba, etc? Of course, it’s a lie. They must think we’re stupid,” tweeted Mr. Giuliani.

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