Is the professor the same person as Susan from the Narnia books?

The professor does seem to be the same person as Susan from the Narnia books, yet she is also separate from the books. Like Susan, the professor's family died in a train crash, and the professor refers to her brother as Ed, which is likely the same Edmund as in the Narnia books. She also dreams about Narnia, and seems very bitter towards Aslan. This seems too much co-incidence for her not to be Susan. Greta also comes to the conclusion that the professor is Susan. However, this is never actually stated, only implied. It is also odd that the professor and Greta talk about the Narnia books. The professor seems to exist as a character from the books, but also as a person outside of the books. She is a real person, but at the same time seems to be aware that she is a literary construct.