If I'm a NJ resident and I went to a credited university from puerto rico and I received the 1098-T for over $4000 of tuition paid, can I claim AOTC credit for $2,500?

Nothing you have said (NJ resident, school in PR)  would disqualify you from claiming the AOTC.  But, there's more to it than that.

There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit. 

You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.

Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863

 See Also see this TT FAQ https://ttlc.intuit.com/questions/3383321-why-didn-t-i-get-a-credit-or-deduction-for-education-expen...

Other references:

 https://www.irs.gov/Individuals/AOTC

https://www.irs.gov/newsroom/american-opportunity-tax-credit-questions-and-answers

https://www.irs.gov/credits-deductions/individuals/education-credits-questions-and-answers

https://ttlc.intuit.com/community/college-education/discussion/i-have-a-1098-t-form-that-i-received-from-my-school-and-i-entered-all-the-information-but-it-said-i/01/998249#M23054