Whenever any such lands shall revert and escheat to the State of Nebraska, as provided in sections 76-403, 76-405, and 76-411, it shall be the duty of the county attorney of the county in which such lands are situated, to proceed against such alien in the district court of the county where the land is situated for the purpose of having such forfeiture declared. The nonresident alien defendants shall be served in the manner provided for the service of a summons in a civil action, and the court shall have power to hear and determine the questions presented in such cases and to declare such lands escheated to the state. When such forfeiture shall be declared by the district court, it shall be the duty of the clerk of the court to notify the Governor of the state that the title to such lands is vested in the state by the decree of the court. The clerk of the court shall present the Director of Administrative Services with the bill of costs incurred by the county in prosecuting such case, who shall issue a warrant to the clerk of the court on the state treasury to repay the county for such costs incurred. The heirs or persons who would have been entitled to such lands shall be paid by the State of Nebraska the full value thereof, as ascertained by appraisement upon the oaths of the judge, treasurer, and clerk of the county where such lands lie, and such lands shall become subject to the law, and shall be disposed of as other lands belonging to the state; Provided, the expense of the appraisement shall be deducted from the appraised value of the land.