In the event a rehearing of any such cause or proceeding is allowed by the Court of Appeals or Supreme Court or if for any other reason the appellate court needs or desires the use of such original bill or bills of exceptions or testimony in equity and law cases, it may order the return of the same to it, and it shall be the duty of the clerk of the court in whose custody the same may be to transmit the same to the Clerk of the Supreme Court upon being personally served with a copy of such order of the appellate court, duly certified under the seal of the appellate court. The expense of the transmittal of such bills and testimony and the costs made in recording, certifying, and serving such order shall be taxed to the unsuccessful party to such suit or proceeding unless the appellate court orders otherwise. The party at whose instance such expense of transmittal is to be made shall advance the same to the clerk if required by him or her. Service of the certified copy of the order may be made by any person. If done by the sheriff of any county, his or her official return shall be sufficient evidence of the fact of service. If by any other person, the service shall be sufficiently proved by his or her affidavit to the fact.