I have a sorcerer who found a wizard's spellbook. She cast read magic and wanted to put some of her spells into the book for the wizard. Is this possible?
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By RAW? No
It says "wizard" explicitly, so by a direct RAW reading of the rule, no. A Sorcerer can't do it.
It also says a wizard can copy into her spellbook, not into someone else's book. That makes sense, as it's hard for a wizard to decipher someone elses magical writing (and your spellbook is meant to be your writing).
A Wizard can add spells to their book from a scroll, so a Sorcerer with Scribe Scroll could create a scroll the Wizard could then use to put it in their book.
Your DM Could Allow It
All that said, if your DM wanted to allow it? It's not a big deal.
I'd probably allow it if a Sorcerer in my game wanted to do it. They still have to pay the cost to write into the book (100g per page of the spell), and it's not exactly giving the Wizard something they can't get elsewhere anyway.
Sometimes, getting hung up on the little details isn't worth the effort. IMO, this is likely one of those times.
How would you go about allowing it? Here's a few ideas on how it might work if your DM wanted to do it: