I'm pretty sure this is a myth.
I think some people get this idea that shaving makes it grow faster and thicker because from the point boys start shaving at 14 or whenever, over time they have to shave more frequently and cut thicker bristles. However, this is just because ageing from puberty to adulthood causes your beard to become thicker and grow faster. Suggesting it's because of shaving itself is putting the cart before the horse.
Bear in mind hair growth can increase when puberty is finished, and well into old age in some cases: your beard can carry on getting thicker, you get more body hair, longer eyebrows, ear hair, and nose hair. Enjoy.