There’s an original post about this here PF2 Spellbook for a Magus/Wizard but I noticed it was in the General Forum and I think this forum is probably more appropriate for raising this issue.
To summarize, currently if you are an arcane prepared spellcaster and you take a dedication for another arcane prepared spellcaster you end up with 2 separate spellbooks. However, you should have one shared spellbook for all your arcane spells:
“If you have a spellbook from multiple sources (such as being a magus with the Wizard Dedication feat), you can use the same spellbook for all your spells.”
Right now I have a Magus with the Wizard Dedication and I have to dupe all my Magus spells into my Wizard spellbook and vise versa if I want to be able to prepare any of my arcane spells in any of my spell slots.
