Illinois has the money so you will have to get it back from Illinois.
This involves filing a non-resident tax return for Illinois where you will enter your W2 but tell the system that you did not live in Illinois. You will qualify for a full refund of your taxes paid to Illinois because of their reciprocity agreement with Wisconsin.
Then AFTER you have done your non-resident return for Illinois, you will do your resident return for Wisconsin. You're going to owe Wisconsin a bunch of money - probably including some penalties - although with any luck what you owe will be less than the refund you're going to get from Illinois.
@sebastiancevasco
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