Yes, she can claim the LLC, if the school is an eligible institution (many foreign schools are not).
Enter your school at the link below, to see if it's on the dept. of education list.
https://www.savingforcollege.com/eligible-institutions
If the school is an eligible institution, you can treat the 529 distribution as a qualified distribution, to the extent that you have net adjusted qualified educational expenses (AQEE). You can NOT count the tuition she uses to claim the LLC (it takes $10,000 of tuition and fees to get the maximum $2000 LLC). The LLC is non refundable. That is, it can only be used to offset an actual tax liability on her tax return.
Room and board, books, other course materials and a computer are not qualified expenses for the LLC, but they are for the 1099-Q/529 distribution.
If you have sufficient AQEE, you do not need to enter the 1099-Q on your return (or hers). If some of the distribution earnings will be taxable, it goes on your return, not hers. You are the "recipient".
