Upvote:6
Yes she will be able to travel to the USA on her permanent resident card although she’s been away an extended period. Immigration at the airport in the USA have no choice but to admit her because abandonment of permanent residency is only determined by an immigration judge.
The worst which can happen is that at the airport immigration charges her with abandoning her status and ask her to appear before an immigration judge to determine if that is the case.
In my opinion the probability of this happening is up in the air. If you tell them at the airport you intend to abandon permanent residency, the most likely outcome is they make her fill out the forms there and then grant her temporary admission/parole to the USA for a few months to do what you’re coming for.
It is extremely unlikely she will be refused entry. They actually don’t have the power to do so to a permanent resident although they might hold you up for a few extra minutes.
Alternatively you can abandon the green card before your trip and use ESTA or apply for a visa.
Reference
I personally know a few people who left the USA to return to my home country for good but things didn’t work out and they returned without a returning resident visa, sometimes two years after leaving. None of them were even put into removal proceedings, go figure!
Applying for ESTA, or any travel document (vacation) as an ex US Permanent Resident Card holder