Flight Instructor conducting a practice approach to a non-towered airport reported a NMAC with a helicopter which overtook them and was not communicating on CTAF.

Narrative

Aircraft X was on a training flight. The RV12 turned established on the Localizer XX into ZZZ. On ADSB In indicated a UH-60 north east and across the location X; trending towards ZZZ1 as is the normal occurrence for those A/C. Seeing what looked like 3 miles of lateral clearance; the approach was continued and commenced with initial descent. We lost sight of traffic; but the ADSB In showed the UH-60 had turned southbound behind us; and trending away from our flight path. Assuming continued separation; the approach continued. Approximately 3 miles out on final and at 2200ft MSL; traffic avoidance alerted to minimal separation and we turned our heads back to see the UH-60 behind and directly under us with minimal lighting at approximately 2000ft Further analysis of ADSB history shows the helicopter had turned and vectored to follow our flight path; closing separation laterally and vertically well out of our line of sight and without making calls on local CTAF for ZZZ. It should be noted this was well out of the flight path this organization typically uses; and was at around pattern altitude on a 3 mile final for an airport whose CTAF they were not announcing calls or intending to land at. I believe the UH-60's failure to communicate on ZZZ CTAF contributed; as well as lack of scanning for traffic in their immediate area. We could have broken off our instrument approach as well; however reaction time would have been limited due to the speed advantage the helicopter had over the RV.