There is no evidence in the emails that Mr. Sater delivered on his promises, and one email suggests that Mr. Sater overstated his Russian ties. In January 2016, Mr. Cohen wrote to Mr. Putin’s spokesman, Dmitri S. Peskov, asking for help restarting the Trump Tower project, which had stalled. But Mr. Sater did not appear to have Mr. Peskov’s direct email, and instead wrote to a general inbox for press inquiries. The project never got government permits or financing, and died weeks later. “To be clear, the Trump Organization has never had any real estate holdings or interests in Russia,”...