When any case or proceeding in which the record or transcript has been so made up has been finally determined in the Court of Appeals or Supreme Court, the original bill or bills of exceptions shall be by the Clerk of the Supreme Court transmitted to the clerk of the district court from which such case or proceeding was removed. It shall be the duty of the clerk of the district court to preserve such bill or bills of exceptions in the files of the office for a period of ten years from the time of receipt from the Clerk of the Supreme Court. After the lapse of such time, if the record in the district court does not show any unfinished matter pending in the case and upon such notice as the district court may direct, such bill or bills of exceptions may be removed from the files and disposed of in any way that the judge of the district court directs when approval is given by the State Records Administrator pursuant to the Records Management Act.