The successor in office of any judge, mayor or other officer who entered lands under said laws of the United States, or who was trustee for the execution of the trust in that behalf, whether such officer or trustee acted under this chapter, or under any other general law, or any local or special act relating to any city or incorporated town, shall succeed to the trust, and shall have authority to execute the same as fully as his predecessor, the original trustee, might have done while in office; and when a mayor’s or other trustee’s deed of any block, lot, share or parcel of any such town site has been lost or can not be found, and there is no record thereof in the office of the county recorder, such successor, upon application to him in writing, duly verified, showing that no mayor’s or other trustee’s deed can be found to the part or parcel of such town site described in the application, and that no such deed thereto is of record in the office of the recorder of the county, and that the applicant, his ancestor, predecessor or grantor has been in the quiet, peaceable and undisturbed possession of said premises under claim of title for the full period of five (5) years next before the application, must, by good and sufficient conveyance, grant and convey the title of the premises described in the application to the applicant, which conveyance must be executed and acknowledged, and shall take and have effect as provided by section 58-802[, Idaho Code], for which and the acknowledgment thereof the trustee shall be entitled to receive a fee of five dollars ($5.00) from the applicant: provided, that in every such application for a deed under the provisions of this section, where an adverse claim to such parcel of said town site shall be made to such mayor for the same, the mayor in every such case shall remit the parties claiming deeds to the same to a court of competent jurisdiction to settle the same, and when so determined, then the said mayor shall execute such deed to the prevailing party.