PA28 Flight Instructor reported while on base; they received a TCAS advisory then observed a helicopter pass below them; resulting in a NMAC event.

Narrative

I was doing landing practice with my Student in the pattern at ZZZ; as we turned downwind a helicopter made a call that they we inbound 5nm to the north; low level. They said that they were headed around to the East to join Taxiway 1 to the ramp. I continued with my Student - they had flight controls at the time - on downwind and gave a radio call that we were on downwind and will be conducting a touch n go. We continued on our pattern and my Student began to turn base; making a call as she turned. At about the same time; the helicopter made a call that they were crossing the extended centerline of Runway XX. As we rolled wings-level on base I scanned for the helicopter to see where it was located. As I did so; the ADS-B let out a warning for traffic; 12 o'clock; one mile. I took controls from my Student and entered a climb and shallow right turn to avoid the traffic. The helicopter made a radio call at about this time that they had 'the base traffic' in sight and that they were going to maneuver to the East to avoid. This caused them to match my turn deconfliction; so I had to turn back to the left (the Northwest). I continued the climb to TPA; and was able to momentarily see the helicopter cross to my low 2 o'clock before going beneath the wing. When I determined the conflict was resolved; I gave controls back to my Student. I am not versed on the airport arrival and approach procedures for helicopter pilots; however it does not seem correct for them to fly across the final approach course of an active Runway with multiple aircraft in the pattern.