((a)) A cobelligerent of the United States that consents to the exercise of jurisdiction conferred by with respect to any prize of the United States brought into the territorial waters of the cobelligerent or appropriated for the use of the United States within those territorial waters shall be given, upon proclamation by the President of the United States, like privileges with respect to any prize captured under the authority of that cobelligerent and brought into the territorial waters of the United States or appropriated for the use of the cobelligerent within the territorial waters of the United States.
((b)) Reciprocal recognition shall be given to the jurisdiction acquired by courts of a cobelligerent under this section and full faith and credit shall be given to all proceedings had or judgments rendered in the exercise of that jurisdiction.