Yes, if taxes were withheld by the IL company and your husband had not physically worked in IL then the taxes were withheld "in error". However, since your husband did have some days working in IL, taxes did need to be withheld. You will have to allocate based on the days working in IL.
You will need to figure out the total days available to work between 9/21 and 12/21 (this excludes weekends/holidays). Divide the income by that number of days and then multiply that result by the number of days actually worked in IL. This will be the wage income allocated to IL.
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