Yes please come hang with him in the library! It is a really cool place to be. Also re: his past, if he and John talked about it before like 200-300ish years in, he would remember everything and be very open about it, he's not shy about discussing his stuff. But by 800 years he's forgotten most of his pre-Abraxas time, though he remembers he knows Geralt from "before" and they have a long history. He supported him through the memory wipe so it would be known he cares a lot about Geralt and he and John could keep that in common.
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LET JESPER HELP YOU FIND LOVE, JOHN.