PA-28 Safety Pilot reported engine power loss during cruise flight. Power was restored after safety pilot directed the student to switch fuel tanks.

Narrative

This report details the priority call; on Day 0 from Aircraft X with ZZZ Approach Control. On this day; I agreed to be a safety pilot for a student at the flight school; while they flew 'Under the Hood'. This was my first time acting as a safety pilot for this student. They were issued a Piper PA28-181. Our plan was to fly to ZZZ; ZZZ1; which was approximately 51 miles from our location. From the beginning; I must confess; I have only had 1 familiarization flight; and 2 additional flights in this type of aircraft; however; I was very proficient with its avionics. One of the things I noticed right off the bat; before taking off; was that the student did not have a checklist for this aircraft; and so I pulled out the POH to at least verify the speeds of the aircraft; while they proceeded to 'download' a checklist on their iPad. After fueling; we took off real close to XA00z. Immediately I noticed that they were was not using their airspeed indicator to climb via Vx or Vy; but simply establish a 500 FPM climb. I also noticed they did not use the turn coordinator to make standard rate turns; and after questioning them about it; I come to understand that they did not understand the basic fundamentals of the turn coordinator.We proceeded to ZZZ; flew the ILS for Runway XR and completed 1 full stop landing; and then proceeded to fly the approach 2 more times; with 1 touch and go; and 1 missed approach; with the intention of proceeding back to ZZZ2. On the way back; we established with ZZZ Center that we would like the RNAV GPS YYR approach into ZZZ2; beginning at ZZZZZ; and were 'Cleared Direct; ZZZZZ' by the Controller. Approximately 5 NM approaching ZZZZZ; at approximately 2000 MSL / AGL the engine begins to 'sputter' and lose power. It appeared the student began to panic; and did not follow any checklist; or execute the simple ABCD's (Pitch for best glide; identify best place to land; complete checklist; or declare an emergency). I assumed control of the aircraft; pitched for best glide speed; and steered the aircraft to line up with the highway which was the closest; 'safe' place to land. After checking the throttle mixture settings; and looking at the instruments I could see from my seat; I decided to call for [priority handling]. I could not see the fuel indicators; as they were on the far side of the instrument panel; and the panel did not have adequate lighting for me to see it from my position; anyway.After calling; and declaring my intentions to head for the highway; a voice came over the radio and said 'check the fuel system.' At this point; I asked the student if they had switched the tanks. They did not respond to this question; so I then instructed them to 'switch the tank.' They reached down; and I heard the tanks switch; and within a couple of seconds; the engine came back to life; and I immediately pitched for Vy; and the aircraft began to climb. Upon returning to 2000 ft. MSL; I informed the Controller that we regained engine power; and we were headed direct to ZZZ2. The Controller asked if we were in need of any emergency services; and I replied that we did not. We proceeded direct to ZZZ2; following normal traffic procedures; and landed on [Runway] YYR at ZZZ2; safely; and without incident. Following this incident; I reviewed the incident with an instructor; and the owner of the flight school; and agreed to a ground safety class regarding fuel system management; and CRM with an emphasis on making better PIC decisions when flying with people I don't know.