N.M. Stat. § 66-5-20
Replacement licenses.
In the event that a permit or driver's license issued under the provisions of this article
is lost, stolen, mutilated or destroyed, or in the event of a name or address change, the
person to whom the permit or driver's license was issued may, upon payment of the
required fee, obtain a replacement upon furnishing proof of age and identity satisfactory
to the department. A person who loses a permit or driver's license and who, after
obtaining a replacement, finds the original, shall immediately surrender the original to
the department.