NEW EVIDENCE in the Ukraine affair has revealed several important new facts. One is that President Trump’s firing of U.S. Ambassador to Ukraine Marie Yovanovitch last spring was part of an explicit trade-off with a corrupt Ukrainian prosecutor who promised dirt on Joe Biden. Another is that Mr. Trump’s demand that Ukraine’s president announce an investigation of Mr. Biden, along with the threat of retaliation if he did not, was communicated to the Ukrainians months earlier than previously known.

The new evidence significantly bolsters the case that Mr. Trump abused his office. It also underlines how much more there is still to learn about the dealings he and his attorney, Rudolph W. Giuliani, undertook in Kyiv, even as the president’s trial on impeachment charges is set to begin in the Senate on Tuesday.

Much of the new evidence comes from Lev Parnas, a former collaborator with Mr. Giuliani and donor to Mr. Trump who turned against them after his indictment on federal campaign finance charges. The White House dismisses Mr. Parnas as a man with a motive to lie, and it’s true that some of his allegations need verification. But the Soviet emigre businessman also gave House investigators texts, emails, calendars and other documents that appear to substantiate key charges.

Texts between Mr. Parnas and Yuri Lutsenko, a former Ukrainian prosecutor, make clear that Mr. Lutsenko made allegations about Mr. Biden in the expectation that he would be rewarded with the firing of Ms. Yovanovitch, who had accused him of blocking corruption investigations. “If you don’t make a decision about Madam — you are bringing into question all my allegations. Including about B,” one Lutsenko text to Mr. Parnas read. He got his wish: “He fired her again,” read a text from Mr. Giuliani to Mr. Parnas in April, shortly before Ms. Yovanovitch was recalled on Mr. Trump’s orders.

Mr. Parnas told MSNBC’s Rachel Maddow that he also played a key role in conveying Mr. Trump’s demand for an investigation of Mr. Biden to Volodymyr Zelensky, who became Ukraine’s president last May. Mr. Giuliani had sent Mr. Zelensky a letter asking for a meeting but called off the trip after it was publicized. Mr. Parnas said he was then dispatched by Mr. Giuliani in early May to deliver a tough message to an aide to Mr. Zelensky: Unless he announced a Biden investigation, relations would sour, starting with the cancellation of Vice President Pence’s attendance at Mr. Zelensky’s inauguration.

Mr. Parnas has produced a note he made on hotel stationery — “get Zalensky [sic] to Annouce [sic] that the Biden case will be Investigated” — and his story is also backed by testimony during the House impeachment inquiry, according to which Mr. Trump told Mr. Pence to cancel his trip to Ukraine the day after Mr. Parnas said he told Mr. Giuliani that the Ukrainians were not responsive.

Mr. Parnas insists Mr. Trump knew all about his activities in Ukraine, as did Mr. Pence, Attorney General William P. Barr and Secretary of State Mike Pompeo. He didn’t offer proof. But given the evidence he did deliver, the need for the Senate to conduct a thorough trial, with testimony from witnesses in a position to confirm or deny the allegations, has become ever more urgent.

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