Chametz on Yom Tov Acharon Shel Pesach

Shalom aleichem Rabbi Lauffer. Thank you for answering my last question. If an American living in America sold his chametz to a non-Jew before Pesach, but then went and bought chametz from the store on the last day of Pesach (Yom Tov Sheni shel Galuyos), would that chametz be forever assur ba’hana’ah, or would it not be because de’oraisa the Pesach was already over in Eretz Yisrael. Thanks a lot.