PA-18 Flight Instructor reported elevator damage found during subsequent student's preflight inspection.

Narrative

Local seaplane training flight in a Piper PA-18-150 Supercub on amphibious floats. The student was getting instruction from me to add-on a single-engine seaplane rating to his commercial pilot certificate; it was our 3rd training flight. The flight was mostly on water operations with multiple takeoffs and landings on ZZZ. Water conditions were fairly calm but not glassy with about 5-7 knots of wind out of the northwest. The flight was uneventful and I basically did not have to touch the controls for most of the flight. All takeoffs and landings were smooth and no anomalies were noticed by myself or the student. The flight ended back at ZZZ1 with no incidents.Preflight inspection of the aircraft by the next student discovered a failure of the furthest outboard section of the right elevator just past the hinge point. The student found this failure approximately 30 minutes after the conclusion of our flight. We cannot be certain that the failure existed or occurred during our training flight; as no abnormal aircraft handling characteristics were noted by me or my student. However; based on the timeline; it is probable the failure could have existed or occurred during our flight. The cause of the failure is unknown at this time.