N.M. Stat. § 45-3-702
Priority among different letters.
A person to whom general letters are rightly issued first has exclusive authority
under the letters until his appointment is terminated or modified. If, through error,
general letters are issued to another, the first rightly appointed representative may
recover any property of the estate in the hands of the representative subsequently
appointed, but the acts of the erroneously-appointed personal representative done in
good faith before notice of the first letters are not void for want of validity of
appointment.