Yes, you can claim whatever amount you paid for his qualified education expenses.
The program will then ask if he "received Veterans Education Benefits?" The only amount you report in this screen is that part of your VA payments that were used for qualified education expenses.
From IRS Publication 970:
If you qualify for one or more of the education benefits discussed in chapters 2 through 13*, you may have to reduce the amount of education expenses qualifying for a specific benefit by part or all of your VA payments. This applies only to the part of your VA payments that is required to be used for education expenses.Example.
You have returned to college and are receiving two education benefits under the latest GI Bill: (1) a $1,534 monthly basic housing allowance (BAH) that is directly deposited to your checking account, and (2) $3,840 paid directly to your college for tuition. Neither of these benefits is taxable and you do not report them on your tax return. You also want to claim an American opportunity credit on your return. You paid $5,000 in qualified education expenses (explained in detail in chapter 2). To figure the amount of credit, you must first subtract the $3,840 from your qualified education expenses because this payment under the GI Bill was required to be used for education expenses. You do not subtract any amount of the BAH because it was paid to you and its use was not restricted."
