Whenever the term of office of any judge of the district court, county clerk or other county officer has expired or may expire, leaving unfinished business which is proper matter of record, or incomplete records, it shall be lawful for the immediate successor of such officer, in any case where written memoranda or copies of any such unfinished business or incomplete records may exist, to complete any such unfinished business or incomplete record from such written memoranda or copies, and make the same matter of record in his or her office; and such records shall be lawful evidence as fully as if the same had been made by such late officer; and in any such case the compensation therefor shall be collected from such late officer, or upon his or her official bond.