MMU Tower Controller stated adjacent facility airspace released control to enter CDW airspace without reference to traffic; resulted in NMAC. MMU Controller also stated that this is a continuing problem with coordination with CDW.

Narrative

I was working Local Control. We were landing and departing Runway 23 and Runway 13. MMU and Caldwell (CDW) Tower have overlapping Class D airspaces. Additionally; MMU Runway 23 final approach course transits the west side of CDWs Class D.I accepted a handoff 10 miles northwest of MMU on Aircraft X. The aircraft data block showed VAA or visual approach to the airport. As Aircraft X was on the visual approach they would need to transits CDWs airspace on final. I initiated a point out with CDW on the shout line and it was approved allowing Aircraft X to enter their airspace. Approximately 7 miles northeast of MMU Aircraft X checked in on tower frequency. At the same time I noticed a VFR aircraft with an ADS-B; Aircraft Y in the southwest portion of CDWs airspace heading northwest bound climbing through 013 MSL. The aircraft was a half mile from the final approach course for Runway 23 and appearing to be a direct conflict with Aircraft X on final. I immediately issued traffic to Aircraft X on the aircraft off their 10 o'clock and half a mile climbing through 016 MSL northbound. Aircraft X responded with looking for traffic. About 5 seconds later since Aircraft X did not have the other aircraft insight and they were converging I told Aircraft X to stop their decent and climb to 020 MSL immediately. Additionally; I reissued the traffic to Aircraft X as Aircraft Y was now flying underneath them and 200 feet below. Aircraft X advised they were now responding to a TCAS RA. After Aircraft X executed the evasive maneuver I asked if they could continue to the approach and they said they could continue. Aircraft X then said tower if you did not point that traffic out to us that definitely would have been a mid air.Approximately 15 seconds later Aircraft Y called up while already in MMU airspace requesting a transition westbound. Aircraft X landed Runway 23 without further incident and Aircraft Y continued on their flight. Aircraft Y did not get approval to enter MMU airspace prior to entering.This is the second instance of this exact scenario in the past 30 days involving CDW and VFR vs IFR on final for Runway 23.Recommendation: I recommend that CDW tower ensures traffic under their control exiting their Class D is aware and de-conflicted from aircraft they have approved through their airspace. This is a recurring issue.