A lawyer for President Donald Trump arranged a $130,000 payment to a former adult-film star a month before the 2016 election as part of an agreement that precluded her from publicly discussing an alleged sexual encounter with Mr. Trump, according to people familiar with the matter.

Michael Cohen, who spent nearly a decade as a top attorney at the Trump Organization, arranged payment to the woman, Stephanie Clifford, in October 2016 after her lawyer negotiated the nondisclosure agreement with Mr. Cohen, these people said.

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