Box 29 only includes the refundable portion of the American Opportunity Credit, which is 40% of the total credit. The remainder appears on Schedule 3, Line 3, which feeds into Form 1040 Line 20. By my math, if the refundable portion is 744, the total American Opportunity Credit is $1,860. That is your Box 1s - Box 5s + 84 for books.
You can get the remaining 640 of credit, but you would have to make $2,140 of scholarship taxable on her return. The terms of the scholarship or grant must allow it to be used for expenses other than qualified education expenses to use this potential tax-saving technique. To do this, just reduce the box 5 amount by $2,140 on your return.
On her return, she would have to claim that $2,140 as income if it was not used for qualified education expenses. She can answer Yes to Did you pay room and board with a scholarship or grant? and enter $2,140 if her scholarship allows. This will enable you to maximize the American Opportunity Credit on your own return.
