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WASHINGTON — An American lobbyist was sentenced Friday to three years of probation and a $5,000 fine for failing to register as a foreign agent for a Russia-friendly political party in Ukraine and for helping a Ukrainian billionaire illegally purchase tickets to President Trump’s inauguration.

The case against the lobbyist, Samuel Patten, highlighted how the Ukrainian political party sought to gain influence in the United States by hiring American consultants who could lobby on their behalf and make connections to the new Trump administration.

Mr. Patten, a longtime Republican operative whose family was once part of Washington’s social elite, pleaded guilty to violating the federal Foreign Agents Registration Act, which requires lobbyists for foreign interests to disclose their work to the Justice Department. Federal prosecutors stepped up enforcement of the often-ignored law in lock step with the investigation of Russian interference in the 2016 election by the special counsel, Robert S. Mueller III.

“The crimes that I committed are a source of great shame and regret for me,” Mr. Patten, 47, wrote in a letter to Judge Amy Berman Jackson of the Federal District Court in Washington. “I should be punished for this.”

Judge Jackson said she was most disturbed by Mr. Patten’s misstatements to the Senate Select Committee on Intelligence about his work in Ukraine and his purchase of the inaugural tickets. She also said his failure to register as a foreign lobbyist for Ukraine was not “a mere technicality” or an oversight, but a serious omission that deprived the American public and members of Congress of information necessary to judge the motivations of lobbyists.

“People need the facts for democracy to work,” she said.

Mr. Mueller’s prosecutors uncovered evidence of Mr. Patten’s offenses while investigating Paul Manafort, the former Trump campaign chairman who was recently sentenced to seven…