Though Mr. Parnas played a key role in the events that led to the former president’s impeachment, the charges he faces involve accusations of campaign finance violations.For Lev Parnas, a Ukrainian American businessman living in Florida, 2018 was a busy year.Sometime around March, he began showing up at Republican fund-raisers. Then, in late April, he dined on cheeseburgers and wedge salads with President Donald J. Trump.By May, a fledgling energy company that Mr. Parnas started with a partner, Igor Fruman, was listed as giving $325,000 to a pro-Trump super PAC. Soon, Mr. Parnas was assisting President Trump’s personal lawyer, Rudolph W. Giuliani, as he oversaw a shadow diplomacy campaign to investigate Joseph R. Biden Jr., then a leading Democratic presidential candidate.Within a year, Mr. Parnas was under investigation, and in late 2019 he was arrested with Mr. Fruman at Dulles International Airport, where both held one-way tickets on a Lufthansa Airlines flight to Frankfurt.Now, Mr. Parnas is facing a trial on campaign finance charges that include contributions to the super PAC and a state candidate in Nevada, where he wanted to operate a cannabis business. And though the case has little to do with his dealings with the former president — who was not accused of wrongdoing in the matter — Mr. Trump’s shadow hangs over Mr. Parnas’s trial, which begins Tuesday in federal court in Manhattan.The trial is expected to fill in gaps in the story of Mr. Parnas’s improbable ascent and downfall, from humble beginnings in Brooklyn to playing a key role in a sequence of events connected to the impeachment of Mr. Trump over accusations that he had asked Ukraine to investigate unfounded allegations about Mr. Biden and a conspiracy theory that Ukraine, rather than Russia, had meddled in the 2016 election.“Parnas is an interesting figure because in many respects he was in the underbelly of the Ukraine story,” said Daniel S. Goldman, the House Intelligence Committee lawyer who led the Ukraine inquiry. “We understood that Parnas in particular was Giuliani’s liaison to a lot of the significant officials in Ukraine.”According to an indictment unsealed after the airport arrests, Mr. Parnas, along with Mr. Fruman and two other co-defendants, conspired to circumvent the federal laws against foreign influence “by engaging in a scheme to funnel foreign money to candidates for federal and state office.”Mr. Fruman pleaded guilty last month to soliciting a campaign contribution from a foreign national. Another co-defendant, David Correia, pleaded guilty last year to conspiracy to commit wire fraud and to making false statements to the Federal Election Commission.Igor Fruman, center, pleaded guilty in September to soliciting a campaign contribution from a foreign national.Go Nakamura/ReutersWhen jury selection begins on Tuesday, Mr. Parnas’s only remaining co-defendant will be a man named Andrey Kukushkin. He is described in court papers as a partner in the planned cannabis business and a participant in a conspiracy to make political donations using money from a rich Russian businessman, Andrey Muraviev.A prosecutor, Hagan Cordell Scotten, suggested during a recent court hearing that Mr. Parnas could be viewed as “something of a genius serial fraudster.”One man who lost money by investing in a company led by Mr. Parnas remembered him wearing diamonds and driving a Rolls-Royce. But behind the trappings of affluence was a history of debts and aborted businesses.As he entered the world of political donors, Mr. Parnas seemed to see it in purely transactional terms, using money to gain access to Republican influencers, then apparently hoping to use those connections to further various moneymaking efforts.While working with Mr. Giuliani in late 2018 and 2019, Mr. Parnas traveled to Kyiv to press officials there to investigate Mr. Biden’s son Hunter, who had served as a board member of a Ukrainian energy company.Records released by Mr. Parnas show that he maintained regular communication with Yuriy Lutsenko, then Ukraine’s chief prosecutor, who was urging the removal of the United States ambassador in Kyiv and promising to help obtain information about both Bidens.Mr. Parnas also exchanged text messages with a Trump ally, Robert F. Hyde, that appeared to include references to people conducting surveillance on the ambassador, who Mr. Trump eventually recalled from her post. Mr. Giuliani later said in an interview with The New Yorker that he wanted that ambassador, Marie Yovanovitch, “out of the way” because he feared she would complicate his attempts to dig up dirt on Joe Biden.After Mr. Parnas’s arrest, Mr. Trump denied knowing him. Before long, Mr. Parnas reversed his loyalties, saying he regretted trusting Mr. Giuliani and Mr. Trump and providing documents, including some related to Ms. Yovanovitch, to the House Intelligence Committee as part of its impeachment inquiry.Federal prosecutors in Manhattan are investigating Mr. Giuliani’s pre-election activities in Ukraine. He has denied wrongdoing.The schemes that prosecutors are planning to outline during the upcoming trial seem more brash than sophisticated.The $325,000 donation to the super PAC, America First Action, was made using money that an indictment said Mr. Fruman and others obtained through a private loan, prosecutors have said. Court papers said that the donation was falsely listed in the name of Global Energy Producers, the company Mr. Parnas and Mr. Fruman were starting, because they were eager to “make it appear that GEP was a successful business.”Mr. Parnas is also accused of making a maximum contribution of $2,700 to the re-election campaign of Pete Sessions, a Republican congressman from Texas and a critic of Ms. Yovanovitch, using a credit card registered to an account belonging to Mr. Fruman and another person.And, according to an indictment, Mr. Parnas was part of a conspiracy to make political contributions by a foreign national. As part of that, the indictment said, a businessman — identified by prosecutors in a separate document as Mr. Muraviev — sent $1 million to a bank account controlled by Mr. Fruman “for purposes of making political donations and contributions.”Among candidates who prosecutors said Mr. Parnas promised to support was Adam Laxalt, who in 2018 was running for governor of Nevada and after the presidential election spoke at a news conference announcing a lawsuit by the Trump campaign seeking to overturn Mr. Biden’s victory in the state. (That suit was dismissed by a state court judge for lack of evidence.)Prosecutors said in a recent court filing that Mr. Laxalt became suspicious about the origins of a $10,000 donation to his campaign identified as being from Mr. Fruman, and sent a check for that amount to the U.S. Treasury “in order to avoid continued possession of the illegal donation without returning it to a potential wrongdoer.”In court filings and during a recent hearing, prosecutors and defense lawyers offered some indications of what arguments they might advance and what evidence they could introduce during the trial.Prosecutors wrote that they intended to offer out-of-court statements made by both defendants, as well as Mr. Correia, Mr. Fruman and Mr. Muraviev. Most of those, they added, “were made in electronic communications, such as emails, text messages, and chats using WhatsApp.”Likely witnesses, they wrote, included Deanna Van Rensburg, who served as Mr. Parnas’s personal assistant from about April 2018 until his arrest, and Mr. Laxalt, now vying for the Republican nomination for a U.S. Senate seat.Mr. Parnas’s lawyer, Joseph A. Bondy, suggested during the hearing, on Oct. 5, that he might portray his client as someone with a “relative lack of education” in the area of election law.And a lawyer for Mr. Kukushkin signaled that he planned to portray his client as a victim of Mr. Parnas rather than as his co-conspirator.The lawyer, Gerald B. Lefcourt, described Mr. Parnas in a recent court filing as the perpetrator of a “con” who, along with Mr. Fruman and Mr. Correia, used a “dog and pony show” to dupe Mr. Kukushkin and many others.“They portrayed themselves as well-connected, powerful political power brokers, who could speak directly to the president of the United States, his children, his inner circle,” Mr. Lefcourt wrote. “Of course, it was all a ruse, one big fraud or Ponzi scheme.” More