Instructor Pilot reported the Trainee over controlled a maneuver and put the aircraft in stall. The Instructor was able to regain control of the aircraft. Later; damage to the aircraft was found and the aircraft grounded per Maintenance. The Instructor states the Trainee has not returned to the flight school.

Narrative

I was teaching my new student the use of flaps on his second flight. We were 45 mins into the flight after teaching 4 fundamentals of flight approximately 15 NM northwest of ZZZ airport at 3000 ft. During the whole lesson the student was maneuvering the aircraft with light and gentle input on the yoke. The student had been taught to fly using 3 fingers to maneuver the aircraft in a light and gentle fashion.Student was instructed to pitch down to lower the angle of attack and I was assisting the student in adding 10 degrees of flaps under the white arc (Below 100mph). In a split second the student grabbed the controls with both hands and pushed the yoke all the way forward causing the airplane to pitch down excessively which resulted in an instant stall. I had my seatbelt and shoulder harness on however I was off my seat slightly. I was in complete shock from the event. I grabbed the controls right away and slowly pitched the aircraft to the horizon and regained aircraft control. Retracted the 10 degree of flaps. Looked outside the window at the wings and everything seems fine visually from inside the cockpit. The aircraft flew perfectly as if nothing had happened. I immediately turned the aircraft to ZZZ intending to land ASAP. In the meantime I asked my student why he had done that. He was in quite a bit of shock and said I do not know and couldn't give me an answer. He stayed quite the whole 10 minutes ride back to home airport. After we had landed I inspected the aircraft exterior and did not notice any structural damage and I had explained to the student the consequences and dangers of his action and that it could have resulted in both of us losing our lives. The student left the flight school and we have not heard from him anymore since the event.The same night of the incident I had an A&P Inspect the aircraft to look for any damage. We did not find any damage and continued flying the aircraft for a few more days. On Day 7 I had noticed the flap rails showed some damage as well as some skin deformation on the top of the wings. We had grounded the aircraft since then.I have informed the insurance regarding the damage.