KIEV, Ukraine — After his name surfaced last August in a secret ledger listing millions of dollars in payments from a pro-Russian party in Ukraine, Paul Manafort not only lost his job running Donald J. Trump’s presidential campaign but also assumed center stage in a bizarre internecine struggle among Ukrainian political forces. On Monday, the intrigue took another turn, when a member of Parliament in Ukraine released documents that he said showed that Mr. Manafort took steps to hide the payments, which were tied to Mr. Manafort’s work for former President Viktor F. Yanukovych. The documents included an invoice that...