My son is a fulltime student in WI, Home state is IL. WI withheld WI and IL taxes. I claim him. How does he file his state?

"My son lives in IL but goes to school in WI. His drivers lic. is IL. He worked in WI the entire school year (on campus and did his internship in WI). The school did not hold any state taxes out. The Company he did his internship at withheld WI taxes for the whole internship, but for the first few weeks they also withheld IL taxes, (doubled taxed) until he brought it to their attention. I claim him on my taxes because he is a full time student. How should we file his state taxes? Resident of IL or WI?  He never worked in IL last year, just WI,  I still claim him because he is a full time student.
(His W2 from the internship has IL earnings (even thought they are all WI) and WI earnings.