As BRP stated, the paid segment cannot be combined.

If AA has an interline agreement w/ LAN checked bags can be tagged through to the final destination, as long as the two res meet the minimum connection time. Just have your girlfriend show her LAN itinerary to the checkin agent at SFO and the segment can be manually added to her itinerary.

However, AA cannot check her into her connecting flight. She would have to do that when she arrives in NY.