Couple filed MFJ fed

He lived in PA Jan and Feb

NJ March - Dec

She lived in PA year round 

filed full year resident PA and full year resident NJ 

Received PA notice they owe $2,000 and their income is missing $50,000, but the $50,000 was put in the NJ return. 

Do I have to file them MFS fed and both states? Can they stay MFJ fed and only do MFS states? with part year resident him PA/NJ and full year her only PA?