Can a foreign national or diaspora woman use the Israeli Rabbinical Court?

Yes. If the couple was married in a Jewish ceremony in Israel, the Israeli Rabbinical Court has exclusive jurisdiction under Section 1 of the Rabbinical Courts Jurisdiction (Marriage and Divorce) Law 5713-1953. If married abroad, the court can still exercise jurisdiction when both parties are Israeli citizens or permanent residents, or when both consent to its jurisdiction. A wife who now lives abroad can file through an Israeli attorney and is not required to appear in person for most hearings.