If conflicting claims as to the domicile of a decedent are made in a formal testacy or appointment proceeding commenced in New Mexico, and in a testacy or appointment proceeding after notice pending at the same time in another state, the district court of New Mexico must stay, dismiss or permit suitable amendment in, the proceeding here unless it is determined that the local proceeding was commenced before the proceeding elsewhere. The determination of domicile in the proceeding first commenced must be accepted as determinative in the proceeding in New Mexico.