Por EUA alfândega & Patrulha de Fronteira (CBP)
Can I travel if my name has changed due to marriage, divorce, etc., and my documents are in my old name?
Lawful Permanent Residents (LPR): LPR's who change their name due to marriage or because of any other circumstance may travel using your LPR Card (US Green Card; I551) in your prior name provided you bring proof of your name progression such as; a marriage certificate, a divorce decree or court documents showing a legal name change.
Please check with the country(s) you are traveling to for their entry requirements.
No seu caso, o país dela não terá nenhum problema, já que ela entrará no passaporte de seu país