Per IRS Publication 970 Tax Benefits for Education:
On page 11: Who Can Claim the Credit?
Generally, you can claim the American opportunity credit if all three of the following requirements are met.
Note. Qualified education expenses paid by a dependent you claim on your tax return, or by a third party for that dependent, are considered paid by you.
On page 18:
To claim the American opportunity credit, the student for whom you pay qualified education expenses must be an eligible student. This is a student who meets all of the following requirements.
On page 20: Expenses paid by dependent. If you claim on your tax return an eligible student who is your dependent, treat any expenses paid (or deemed paid) by your dependent as if you had paid them. Include these expenses when figuring the amount of your American opportunity credit.
TIP: Qualified education expenses paid directly to an eligible educational institution for your dependent under a court-approved divorce decree are treated as paid by your dependent.
Expenses paid by you. If you claim a dependent who is an eligible student, only you can include any expenses you paid when figuring the amount of the American opportunity credit. If neither you nor anyone else claims the dependent, only the dependent can include any expenses you paid when figuring the American opportunity credit.
On page 23 regarding Lifetime Learning Credit
Who Can Claim the Credit?
Generally, you can claim the lifetime learning credit if all three of the following requirements are met.
On page 29:
For purposes of the lifetime learning credit, an eligible student is a student who is enrolled in one or more courses at an eligible educational institution (as defined under Qualified Education Expenses, earlier).
Expenses paid by dependent. If you claim on your tax return an eligible student who is your dependent, treat any expenses paid (or deemed paid) by your dependent as if you had paid them. Include these expenses when figuring the amount of your lifetime learning credit.
TIP Qualified education expenses paid directly to an eligible educational institution for your dependent under a court-approved divorce decree are treated as paid by your dependent.
Expenses paid by you. If you claim a dependent who is an eligible student, only you can include any expenses you paid when figuring the amount of the lifetime learning credit. If neither you nor anyone else claims the dependent, only the dependent can include any expenses you paid when figuring the lifetime learning credit.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.