Did Crimean Khanate claim to be a successor to the Mongolian Empire and how prevalent was it?

So I was watching the movie "Potop" (Deluge) which is based on a book that takes place during The Second Northern War and at one point one of the characters reads out a letter from the Poland to Crimea (or vice versa) it mentions that crimea was a "successor to Ghengis Khan" and I'm interested if this was a case or not