Together, parent and child can daydream outloud what animal they would turn into if one was an Animogus. Or secretly wish that one could fake a convincing British accent in order to audition for the movie. Rowling has created a timeless series. I expect that when my son has children they will read the series, and their children also. Like Frank L. Baum, C.S.Lewis and Ron Dahl, Rowling will find her name revered as a writer that was able to reach out and touch a person's imagination and very soul.
Few writers can reach both the young and old for several generations.
I predict that Rowling will have the honor of being among that short list. I bet there are millions of readers around the world right now, young and old, wishing they weren't plain old Muggles.