A determination of the question of fact as to who are the heirs of any deceased citizen allottee of the Five Civilized Tribes of Indians who may die or may have heretofore died, leaving restricted heirs, by the probate court of the State of Oklahoma having jurisdiction to settle the estate of said deceased, conducted in the manner provided by the laws of said State for the determination of heirship in closing up the estates of deceased persons, shall be conclusive of said question: Provided, That an appeal may be taken in the manner and to the court provided by law, in cases of appeal in probate matters generally: Provided further, That where the time limited by the laws of said State for the institution of administration proceedings has elapsed without their institution, as well as in cases where there exists no lawful ground for the institution of administration proceedings in said courts, a petition may be filed therein having for its object a determination of such heirship and the case shall proceed in all respects as if administration proceedings upon other proper grounds had been regularly begun, but this proviso shall not be construed to reopen the question of the determination of an heirship already ascertained by competent legal authority under existing laws: Provided further, That said petition shall be verified, and in all cases arising hereunder service by publication may be had on all unknown heirs, the service to be in accordance with the method of serving nonresident defendants in civil suits in the district courts of said State; and if any person so served by publication does not appear and move to be heard within six months from the date of the final order, he shall be concluded equally with parties personally served or voluntarily appearing.