Incorrect. PA will not give you a tax credit for taxes paid to NJ due to the reciprocal agreement between the two states.
Prepare the non- resident NJ return but show NO income such that you get a full refund of all NJ withholding. I'm assuming your only NJ income is wages.
Then file a PA resident return showing ALL income, including that earned in NJ.
And get the form filed with your employer so no NJ income taxes are withheld next year.
