A Flight Instructor reported they were cleared for takeoff from the runup area but another aircraft took the clearance and taxied past them missing them by less than five feet.

Narrative

Our aircraft was instructed to hold position in the ZZZ Runway XX runup area (West side of the runway) awaiting clearance for takeoff with a planned modified downwind departure in compliance with local noise abatement procedures. We were holding in the runup #1 for departure; with another aircraft holding short of Runway XX on [Taxiway] 1. A Mitsubishi MU-2 was instructed to hold short of the runup behind us #2 for departure; and to leave space for us to pull out. Tower cleared us for takeoff in front of the MU-2; and my student advanced the throttle to begin taxi to the runway for takeoff. As we began moving; the pilot of the MU-2 began taxiing without a clearance in front of our aircraft; with the tip of their right wing coming within 5 feet of our nose. My student immediately applied maximum braking. The MU-2 then began a sharp turn to rotate towards the runway entrance at high power; which caused excessive propwash to effect our aircraft; and directed FOD into our windshield and propeller. The MU-2 pilot requested clearance to take off in front of us while rolling across the hold short line for Runway XX; and was subsequently cleared for takeoff and departed. We departed several minutes later without incident.