PA-28 flight instructor reported a runway incursion by another aircraft while on approach to land on training flight with a student.

Narrative

I was acting as a flight instructor with a student in a Piper Warrior; doing a night cross country flight from ZZZ1 to ZZZ. The entire flight was conducted under VFR flight following; and communication was maintained with ATC throughout. The flight proceeded normally until the final approach into ZZZ. At roughly 10 NM north-west of ZZZ the ZZZ Approach Controller informed us that there was no observed traffic in between us and ZZZ; radar services were terminated and we were to squawk VFR and change to the local advisory frequency. We complied and announced our position and intention to use Runway XXR for pattern work on the ZZZ CTAF. Hearing no response on the CTAF frequency; we proceeded with decent and before landing preparations. We proceeded to announce our position and intention to use Runway XXR several times while on approach to a 45 degree right base-to-final. Due to the runway edge lights creating a glare; we were unable to see that a Hawker 700 had entered Runway XXR and had proceeded to back taxi to line up with Runway XXL. The Hawker 700; then turned around 180 degrees to line up; while we were on final approach to Runway XXR. Throughout the back taxi the Hawker 700 made no radio calls on CTAF. After the Hawker had completed the back taxi; the landing lights were visible and I identified the aircraft's presence for the first time. At this time; we were nearly over the runway approach lights and I called for a go-around. We successfully completed the go-around procedure; and the Hawker 700 did not start the take-off roll. After the go-around; we were on the upwind leg turning to the crosswind leg and I observed the Hawker 700 take-off on Runway XXL and proceed into a climbing left turn. At no point was I able to contact the Hawker 700 on CTAF; and the Hawker 700 made no radio calls on CTAF throughout the entire event. The Hawker proceeded on course and we completed our planned pattern work without incident. Due to the taxi path of the Hawker 700; I do not believe the pilots of the Hawker 700 could have made visual contact with us until we had started our go-around. I am not certain if the pilots of the Hawker 700 ever made visual contact with us. Due to the glare from the runway edge lights; we were unable to identify the position of the aircraft until final approach making a go-around necessary. The Hawker 700 never made a single radio call on CTAF; as a result we were unaware they existed until we made visual contact. After the go-around I briefly monitored another frequency listed for ZZZ Tower; in case the Hawker 700 had mistakenly chosen the incorrect frequency. I do not know which frequency the Hawker 700 was transmitting on; or if the jet was transmitting at all. I suspect the pilots mistakenly used an incorrect frequency; which led to the inability to communicate. I would like to stress that the timing of the event could have led to a near-midair collision. Had we begun our approach roughly 20-30 seconds later than we did; I suspect the Hawker 700 would have begun a take-off roll. This could have resulted in a rejected take-off; and a go-around. Worst case scenario; the jet would have accelerated past V1 and been forced to continue; making both aircraft take aggressive evasive action to avoid a midair collision.