Yes, you should correct the wages in the W-2 section as long as you can substantiate it with the pay stubs. Add another state wage line in the federal interview. The important actions are to report the correct amount of income and tax withholding to the correct state of residency because you moved during the year.
Do NOT change the withholding amounts. The state withholding shown on the W-2 is where the tax was paid.
States vary on filing requirements and is always based on residency and domicile.
Proceed to complete your part year resident state tax returns for both states. Be prepared to show residency change and wages earned in each state should you need that later. The state where the wages are listed on the W-2 may want to see a copy of the other state return later, however sometimes that isn't an issue when both are filed electronically.
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