PA-28 Instructor reported a throttle malfunction during a training flight. The Instructor was able to overcome the problem and return to airport safely for maintenance support.

Narrative

While conducting a practice localizer approach at the ZZZ; I advised my student to reduce power upon reaching the final approach fix. He advised me he was unable to move the throttle and it appeared stuck. I confirmed the throttle was stuck and I was unable to move it from around 1800-2000 RPM. The throttle eventually jarred back very abruptly to flight idle resulting in insufficient power to maintain altitude. I did immediately confirm the throttle friction lock was not the source of trouble. Once again; I had to force the throttle up and once I did; it was responsive and we achieved appropriate RPM once again. I advised CTAF that we were having throttle issues and would make the approach a full stop landing. I kept the power at the setting it was at until the runway was made. Once the runway was made; I had to use an extreme amount of pressure to lower RPM. The alternative plan was to cut the mixture; which was not needed. Upon safe landing; my student and I taxied to the runup area and troubleshot the issue. I was unable to replicate the problem on the ground. The plane was left on the ramp at ZZZ until inspected by maintenance. A squawk sheet was completed and my company was advised.