Okla. Stat. tit. 44 § 229
The Governor is authorized to order the National Guard, or any part thereof, beyond the borders of the state, for the purpose of participating in any encampment, maneuvers or field instruction and for such other training or service as may be required or authorized under state or federal law. Whenever the National Guard, or any part thereof, is so ordered beyond the borders of the state, the members thereof shall remain subject to the military laws and regulations of the state, and the military courts of this state shall have jurisdiction over any offense which is committed against the military laws or regulations of the state by any member of the National Guard while in service beyond the borders of the state, and the military courts of the state are authorized to function beyond the borders of this state, whenever the National Guard is ordered beyond the borders of the state. Provided, that any imprisonment imposed while a unit is out of the State of Oklahoma shall be served under the supervision of said unit. And, provided further, that if said period of imprisonment extends beyond the date of the return of said unit to the State of Oklahoma that the balance of such imprisonment shall be served in accordance with Section 858 of this title (Article 58).
Okla. Stat. tit. 44, § 229