Qualified International University Doesn't Provide 1098-T

[ThisJCD]

My child goes to an international university that is recognized by the US. (They receive a FASFA loan in addition to what we are paying for tuition.)  We made the request, but the school doesn't provide a 1098-T form and doesn't seem to have a federal  ID number (at least the person we talked to wasn't aware of one). They did give us documentation stating what we paid in tuition. However, using TurboTax Deluxe there is no option I can find to claim the American Opportunity Credit w/o the 1098-T and federal ID number. 

I looked at the IRS site and it states we can "claim an educational credit" if we can prove the we made the payments. 
Is the software incorrect, and we are eligible to claim the American Opportunity Credit? How the heck do I claim this expense?

[MonikaK1]

In order for you to claim an education credit on your tax return, the school attended must have been an Eligible Educational Institution. 

An eligible educational institution is a school offering higher education beyond high school. It is any college, university, trade school, or other post-secondary educational institution eligible to participate in a student aid program run by the U.S. Department of Education. This includes most accredited public, nonprofit and privately-owned–for-profit postsecondary institutions.

If you aren’t sure if your school is an eligible educational institution:

• Check to see if the student received or was issued a Form 1098-T, Tuition Statement. Eligible educational institutions are required to issue students Form 1098-T, Tuition Statement (some exceptions apply).
• Ask your school if it is an eligible educational institution, or
• See if your school is on the U.S. Department of Education’s Database of Accredited Post Secondary Institutions and Programs (DAPIP) or the Federal Student Loan Program list.

In general, a student must receive a Form 1098-T to claim an education credit. See here for more information from the IRS on this topic including possible exceptions.