The Commission shall receive and determine, or redetermine as the case may be, in accordance with applicable substantive law, including international law, the validity and amounts of claims owned by persons who were nationals of the United States on September 3, 1943, and July 24, 1968, against the Government of Italy which arose out of the war in which Italy was engaged from June 10, 1940, to September 15, 1947, in territory ceded by Italy pursuant to the treaty of peace with Italy: Provided, That no awards shall be made to persons who have received compensation in any amount pursuant to the treaty of peace with Italy or subsection (a) of this section.