The board voted to reinstate him to his position after the false accusations were proven.

reinstate 是由前缀 re-（表示"重新"）和动词 instate（使就职、任命）组成的复合动词。re- 表示"再次"，instate 来自 state（状态），字面意思是"使回到原来的状态"。reinstate 的意思是"使恢复原职"或"恢复原来的状态"。