Either the student or the parent can claim the American Opportunity Credit.
A student must attest to the fact that he is not a dependent on someone else's return in order to take the credit. The reason is because the law considers the parent as the one who is paying the dependents education expenses, even if the dependent had directly paid the qualified expenses.
The key word is dependent. If you are considering him as a dependent on your return, then he must indicate on his return that someone else his claiming him. This will prevent him from claiming the credit, even if you are not able to because of the limitations associated with the credit.
