N.M. Stat. § 45-3-613
Successor personal representative.
A. Sections 3-301 through 3-311 [45-3-301 to 45-3-311 NMSA 1978] and 3-401
through 3-414 [45-3-401 to 45-3-414 NMSA 1978] govern proceedings for appointment
of a personal representative to succeed one whose appointment has been terminated.
B. After appointment and qualification, a successor personal representative shall be
substituted in all actions and proceedings to which the former personal representative
was a party, and no notice, process or claim which was given or served upon the former
personal representative need be given or served upon the successor in order to
preserve any position or right the person giving the notice or filing the claim may thereby
have obtained or preserved with reference to the former personal representative.
C. Except as otherwise ordered by the district court, the successor personal
representative has the powers and duties in respect to the continued administration
which the former personal representative would have had if his appointment had not
been terminated.