Does puberty stop for a female two years after a regular menstruation cycle?

Not necessarily. Puberty as a sequence of events can last 3 years at the short end and 7 at the longer end. Usually a young woman can only expect to get 2.5 inches taller after first menses because the hormones of puberty tell the growth centers to finish and close. This is often done within 2 years yet subtle changes of puberty may continue for some time.