You firm did report wages correctly from their point of view. Once they moved to New Jersey they became a NJ company and you are a NJ resident, so they would begin to report NJ wages and withholding.
This creates a tricky situation for you because of the way TurboTax is set up. TurboTax allows you to remove duplicate state wages. But your wages are not complete duplicates.
Remove NJ wages from the NJ section and add any difference as an adjustment. For example, if NY shows $100,000 and your company moved mid-year, $50,000 would be a duplicate wage. Suppose NJ reported $52,000 for that period. You would keep $100,000 as your total wage and add $2,000 as an adjustment.
You would still get a tax credit for the wages earned while the company was in NY and you paid NY tax.
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