You always want to enter the W2 information as it appears on the W2. Then, when you get to the NJ return, you will see a screen entitled "About this income". It will show the two lines (NY and NJ) on the screen. You will uncheck the NY box so that only NJ calculates. On a later screen, you will be given the option to claim a tax credit for the income tax NY assesses on the income that must also be reported to NJ from the date you moved there.
New Jersey requires this of tax software programming. It does not allow the programming to automatically filter out the amounts that have been reported on two separate lines, and programming is required to add them together unless they are filtered out. This is how you will do so.
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