Flight Instructor reported while in the practice area they noticed traffic on their TIS-B and this traffic began a climb resulting in the student pilot taking evasive action to avoid a collision with the other aircraft.

Narrative

TIS-B Traffic Advisory ActivationA student and I had just started our flight out of ZZZ. We took off and followed his Nav Log; turning southbound after exiting ZZZ's airspace. The student was performing well; looking for traffic and making all necessary practice area calls. I notice on the TIS-B that there is an aircraft 1200 feet below us; however; the next second this aircraft appeared to be right below us and climbing as caught by my student; and he quickly made an evasive climb to clear the aircraft. I then saw the aircraft on my side; and the aircraft came within 50 feet of vertical distance and didn't know they almost hit us until I told them. I quickly confronted the other aircraft; telling them that their transponder was giving faulty information. They then told me a few important details of information:1. It was the pilots first time taking out that particular airplane.2. ZZZ Tower had told them after they took off behind us that their ADS-B was malfunctioning and indicating 1000 feet lower than it should.3. The aircraft didn't know they had almost hit us until we called them.Flight continued without incident; and the other aircraft reset their transponder which then indicated the correct altitude.The aircraft was close enough that I could make out paint details of the other aircraft. Although they were very cooperative and apologetic about the incident; their actions easily could have gotten us killed by climbing right into our blind spot; in a situation where we have right of way. Their decision to proceed into a highly congested practice area after being told by Tower that their transponder was malfunctioning was a poor decision on their part that could have resulted in an aircraft accident.