Yes your student can claim $1000 American Opportunity credit

and it doesn't metter if she/he has any income. But then you cannot claim him/her as depedent hence losing $500 dependent credit.

https://www.irs.gov/credits-deductions/individuals/aotc#:~:text=The%20American%20opportunity%20tax%20credit,of%20%242%2C500%20per%20eligible%20student.