Yes, since you have not filed the amended return with MN, let the original process, get that money and then file the amended return. Since it shows no balance due or additional refund, you must not be changing your tax liability.
Since you live in WI, you would normally file an amended WI with the additional income and a credit for the MN tax but I am not convinced you need to since there is no change in MN liability, there would be no change to WI either. I don't think it needs to be filed.
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