If your client was a resident of NJ but worked in PA, the reciprocal agreement would have your client's wage subject to tax only in the resident state of NJ and exempt from PA tax.  The PA employer should have withheld NJ taxes instead.  What you should do is to file a PA return to claim a full refund on the PA SIT.  Your client will need to report the wages in full to NJ and have a balance due.

To avoid this problem in 2022, your client should complete an REV-419 and submit it to the PA employer so that proper reporting/withholding will be done going forward.