Under current regulations a legal permanent resident of the United States must return to the U.S. within 364 days of the last departure in order to retain status as a permanent resident. If the person has obtained a reentry permit (form I-327), the person must return to the United States within the validity of the reentry permit in order to retain status as a permanent resident. Reentry permits cannot be extended, and applications are only accepted in the U.S. by the U.S. Citizenship and Immigration Services.

She can file her I-751 from outside of the United States, but will presumably have to return to the United States for biometrics. (Note that she would need a reliable U.S. address, as the USCIS will not send her biometrics appointment information to an overseas address; the location of her biometrics appointment will be based on that address.) If she does that before her reentry permit expires, she can apply for a new reentry permit at that time (it would have to be a new permit - she can't extend the first one). Given the time frame you describe, I don't see how she can avoid applying for a second reentry permit; she may want to consult an immigration lawyer with the details of her situation to see if the lawyer can cook up a work-around.