YES
You can claim expenses for education expenses of the year and the first 3 months of the next year.
However; you might not meet the requirement of having been a full-time student for eligibility of certain credits.
According to the IRS:
“Prepaid expenses. Qualified education expenses paid in 2016
for an academic period that begins in the first 3 months of 2017 can be used in
figuring an education credit for 2016 only. See Academic period, earlier. For
example, if you pay $2,000 in December 2016 for qualified tuition for the 2017
winter quarter that begins in January 2017, you can use that $2,000 in figuring
an education credit for 2016 only (if you meet all the other requirements). “
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HERE for IRS Pub 970 Tax Benefits for Education
