No. All of the tuition credits are only available on the tax return that has claimed the student as a dependent.
If he should have been claimed as a dependent on your return (see below), then your best course of action is to have him file an amended return, selecting "someone else can claim me as a dependent." This opens up the tuition credits and the exemption for you to claim.
If he was allowed to claim himself, he has the option of amending his return and adding the tuition credit.
Here are the 7 tests for claiming a dependent:
1) You provided more than half
of their financial support. More info
2) They made less than $4,050 in gross income
during 2016 unless they are a
qualifying child (under 19 OR a full time student under 24
OR permanently disabled)
3) They live with you or they are related to
you.
4) They are a U.S. citizen, resident alien,
national, or a Canadian or Mexican resident.
5) They aren't (or won't be) claimed as a
dependent by someone else.
6) They aren’t filing a joint return with
their spouse.
7) You are not being claimed as a dependent on
someone else's return.
If you do claim him as a dependent, he will
still need to file his own return and he should answer Yes to "can someone else claim you as
a dependent?"
