After the start of menstrual cycles, does the girl child stop growing taller in height?

Sort of: Onset of menstration starts the fusion of the growth plates and decreases the rate of linear growth, but does not stop it completely.

Still grows but...: Menarche, start of menstruation, follows growth spurt. Girls continue to grow, 3-5 inches more.

Most girls grow: for about 2 years after they start menstruating, but it is a slower growth than prior. The biggest growth spurt is generally during the year before the first period.