It can be claimed 4 times by any student or the taxpayer claiming the student.

If you think you are eligible and claim the credit, the IRS will inform you if you have used it 4 times already.

But be aware, according to the IRS:

“If you claim this credit even though you're not eligible and it's determined that your error is due to reckless or intentional disregard of the rules, but not fraud, you won't be allowed to claim the credit for 2 years. If it's determined that your error is due to fraud, you won't be allowed to claim the credit for 10 years”

Keep copies of the returns and other information you used to investigate if the credit had been used 4 times already, to prove to the IRS that you did your best to research this question, in case you are wrong.