All cases pending in the District Court for the Territory of Alaska at the time said Territory becomes a State not transferred to the United States District Court for the District of Alaska shall be proceeded with and determined by the courts created by said State with the right to prosecute appeals to the appellate courts created by said State, and also with the same right to prosecute appeals or writs of certiorari from the final determination in said causes made by the court of last resort created by such State to the Supreme Court of the United States, as now provided by law for appeals and writs of certiorari from the court of last resort of a State to the Supreme Court of the United States.