Yes. Since the parents are divorced and the 19 year old is still a qualifying child due to being a student, the parent with physical custody (lived with MORE than half of the year) can still claim the EIC for the student, while the custodial parent can still sign form 8332 to allow the non custodial parent to claim the $500 Non-refundable Other Dependent Credit. Generally though, if the student is in college, the parent who claims the child as a dependent is the one who can claim them for education credits.
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