I recently ran out of room in my first spellbook. I added a second one and learned a few spells into that book as well. This all worked fine, and the new spells show up with the rest in the spell descriptions area.
On the second to the last page, where innate and equipment uses per day checkboxes are put, it does something quite odd. I see a list of the two spells in my spellbook #2 with checkboxes next to them. No idea why.
See page 11 attached.
This is expected behavior. You can use the check mark to indicate you learned the spell, or cast it, or whatever you'd like to use it for. Nothing to fix.
If that is the case why would spellbook 2 do this but not spellbook 1? Any caster of a reasonable level will not be able to fit all their spells in one book. At high level with 4 or 5 books this will get really messy. It seems like it should either make checkmark boxes for all spellbooks or none...not this weird in between state.