All appeals taken from the District Court for the Territory of Alaska to the Supreme Court of the United States or the United States Court of Appeals for the Ninth Circuit, previous to the admission of Alaska as a State, shall be prosecuted to final determination as though this act had not been passed. All cases in which final judgment has been rendered in such district court, and in which appeals might be had except for the admission of such State, may still be sued out, taken, and prosecuted to the Supreme Court of the United States or the United States Court of Appeals for the Ninth Circuit under the provisions of then existing law, and there held and determined in like manner; and in either case, the Supreme Court of the United States, or the United States Court of Appeals, in the event of reversal, shall remand the said cause to either the State supreme court or other final appellate court of said State, or the United States district court for said district, as the case may require: Provided, That the time allowed by existing law for appeals from the district court for said Territory shall not be enlarged thereby.