Flight instructor on training flight with student reported a ground conflict with landing traffic.

Narrative

We (Aircraft X) had been established in the traffic pattern at ZZZ using Runway XX with calm winds. My student was instructed to perform a short field landing on XX. Appropriate radio calls were made from our aircraft despite an empty pattern. Turning downwind to base; I noticed an ADS-B target about 4 miles out appearing to be entering the pattern. When turning base to final; I heard Aircraft Y called a short approach to Runway XY; the opposing runway. I keyed the radio and reiterated that we were on final for XX with no response. On a 1/4 mile final I got Aircraft Y in sight on a very short; high final for XY. My student landed the airplane in a flawless short field landing and exited the runway at Taxiway XY. Less than 5 seconds later; Aircraft Y touched down on or beyond the 1000 ft. markers; approximately 500 ft. behind where we cleared the runway. Aircraft Y appeared to lock up the brakes to stop before departing the runway surface. PF (Pilot Flying) and IP (Instructor Pilot) confirm runway currently in use prior to entering the traffic pattern. Abort training events if safety of flight is compromised.