Firstly, In order to stop all the confusion about aircraft C of A, place the aircraft on a Transport Category C of A. This should be a fairly easy process for a C152, providing that the engine has not reached its life. If you are going to leave the aircraft on a private C of A, there is an AIC on the subject, but i can not remember exactly what it says. Best to read it your self
Secondly, the instructor would need to be registered as a JAR training organisation and have agreement to operate under another organisation.
AC&X