When the State is admitted into the Union, and the District Courts in the respective districts are organized, the books, records, papers and proceedings of the probate court in each county, and all causes and matters of administration pending therein, upon the expiration of the term of office of the Probate Judge, on the second Monday in January, 1896, shall pass into the jurisdiction and possession of the District Court, which shall proceed to final judgment or decree, order or other determination in the several matters and causes, as the Territorial Probate Court might have done, if this Constitution had not been adopted. And until the expiration of the term of office of the Probate Judges, such Probate Judges shall perform the duties now imposed upon them by the laws of the Territory. The District Courts shall have appellate and revisory jurisdiction over the decisions of the Probate Courts as now provided by law, until such latter courts expire by limitation.