One of Ben Carson’s top fundraisers told the Republican presidential candidate on Wednesday that he is quitting the campaign after he was unable to orchestrate a shake-up of its senior staff.

Bill Millis, an heir to a High Point, N.C., sock-manufacturing fortune, told the retired neurosurgeon in an email Wednesday morning that he is leaving the campaign’s three-man board, Mr. Millis said in an interview. He still believes Mr. Carson would make the best president, he said, but is no longer confident the staff values his input.

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