During a night of heavy drinking at an upscale London bar in May 2016, George Papadopoulos, a young foreign policy adviser to the Trump campaign, made a startling revelation to Australia’s top diplomat in Britain: Russia had political dirt on Hillary Clinton. About three weeks earlier, Mr. Papadopoulos had been told that Moscow had thousands of emails that would embarrass Mrs. Clinton, apparently stolen in an effort to try to damage her campaign. Exactly how much Mr. Papadopoulos said that night at the Kensington Wine Rooms with the Australian, Alexander Downer, is unclear. But two months later, when leaked Democratic...