SYNOPSIS
A Cessna 172, EI-CUJ, with a solo Student Pilot on board, was given clearance by the Air Movements Controller (AMC) to backtrack and line up on Runway (RWY) 25 at Cork Airport. While EI-CUJ was taxiing, a second Cessna 172, G-GFSA, with a Flight Instructor and Student on board, was given take-off clearance on RWY 35. As G-GFSA was climbing away, the AMC saw that EI-CUJ had become airborne from RWY 25 without clearance.