Okla. Stat. tit. 66 § 56
Either party aggrieved may appeal from the decision of the district court to the Supreme Court; but such review or appeal shall not delay the prosecution of the work on such railroad over the premises in question, if such corporation shall first have paid to the owner of said real property, or deposited with the said clerk for said owner, the amount so assessed by said commissioners or district court; and in no case shall said corporation be liable for the costs on such review or appeal, unless the owner of such real property shall be adjudged entitled, upon either review or appeal, to a greater amount of damages than was awarded by said commissioners. The corporation shall in all cases pay the costs and expenses of the first assessment. And in case of review or appeal, the final decision may be transmitted by the clerk of the proper court, duly certified, to the proper register of deeds, to be by him filed and recorded as hereinbefore provided for the recording of the report, and with like effect. The fee of land over which a mere easement is taken, without the consent of the owner, shall remain in such owner subject only to the use for which it was taken.
Okla. Stat. tit. 66, § 56