Settlers who have unpatented entries under any of the public land laws embracing lands which have been eliminated from the project, or whose entries under water rights have been so reduced that the remaining area is insufficient to support a family, shall be entitled to exchange their entries for other public lands within the same project or any other existing Federal reclamation project, with credit under the homestead laws for residence, improvement, and cultivation made or performed by them upon their original entries and with credit upon the new entry for any construction charges paid upon or in connection with the original entry: Provided, That when satisfactory final proof has been made on the original entry it shall not be necessary to submit final proof upon the lieu entry. Any entryman whose entry or farm unit is reduced by the elimination of permanently unproductive land shall be entitled to enter an equal amount of available public land on the same project contiguous to or in the vicinity of the farm unit reduced by elimination, with all credits in this section hereinbefore specified in lieu of the lands eliminated. Owners of private lands so eliminated from the project may, subject to the approval of the Secretary of the Interior, and free from all encumbrances, relinquish and convey to the United States lands so owned and held by them, not exceeding an area of one hundred and sixty acres, and select an equal area of vacant public land within the irrigable area of the same or any other Federal reclamation project, with credit upon the construction costs of the lands selected to the extent and in the amount paid upon or in connection with their relinquished lands, and the Secretary of the Interior is authorized to revise and consolidate farm units, so far as this may be made necessary or advisable, with a view to carrying out the provisions of this section: Provided further, That the rights extended under this section shall not be assignable: And provided further, That in administering the provisions of this section and section 423a of this title, the Secretary of the Interior shall take into consideration the rights and interests of lien holders, as to him may seem just and equitable: Provided further, That where two entrymen apply for the same farm unit under the exchange provisions of this section, only one whom 1