N.M. Admin. Code § 19.2.3.18
No assignment of a lease or any portion thereof will be made except with the approval of the commissioner upon such terms and conditions as the commisioner may require. All assignments shall be upon forms prescribed and furnished by the commissioner, which shall recite, among other things, the consideration received for the assignment. In the event a lessee desires to transfer a portion of the lease, the lessee may do so with the approval of the commissioner by relinquishing that portion to the commissioner in order that a new and separate lease may be issued to the third party. Any lease in good standing may, with the approval of the commissioner and the payment of a fee as set forth in the schedule of fees, be relinquished to the state of New Mexico.
N.M. Admin. Code § 19.2.3.18