PA and NJ have reciprocity.  File MFJ in PA and a NJ NR/PY return. When you allocate income to the NJ return show only the 3 mos He was a resident. The rest gets reported on the PA return. 

If his w2 shows all withholdings in NJ then claim them in NJ. Likely, overpayment in NJ, underpayment in PA

Moving forward NJ employer should be withholding PA tax.