It starts with Sassacre writing a book of japery, which is handed down the family tree to John. A series of events bringing him to the Medium leave Nanasprite writing the inscription on the book and dropping it on LoWaS for John to pick up. Eventually it makes its way to the ectobiology lab, where it gets sent back in time with Nana to her 'birth' back in olden times. Presumably the respectable southern gentleman gains inspiration from this book and writes the original copy.
Actually, the copy of Sassacre's book with the inscription went back in time with John, Nanna went back with Dad's dirty hat. And I always just figured that what John had was just a copy that Dad bought for him or something. It looks a bit too new for me to think that it was passed down from Sassacre's time, nearly a century before the story starts.
But yeah, with the bunnies Jake and Lalonde got from their guardians, Mutie, Dream Cal, Jane's dirty old hat, and now Poppop's Sassacre book with the exact same inscription John's had? It looks like that when the kids and their guardians were made by John and were then sent through Skaia's portals they were basically copied and become two sets, with one sent to B1 and the other sent to B2. Similar to what (I think at least) happened to allow the Trolls and Ancestors to exist in A1 while only being made in A2's session. Which means that universe B is probably suffering from LE's glitch. Either that, or there are shenanigans at work.