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?
[RPG] Can a sorcerer write their own spells into a wizard’s spellbook in 3.5
No, you can't write the spells you know as a Bard into your spellbook.
There are 2 ways (outside of levelling as a Wizard) that a Wizard can add spells to their spellbook. The first is by finding them:
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it.
What does it mean to "find" a spell? Some examples are given immediately preceding this:
You might find other spells during your adventures. You could discover a spell recorded on a scroll in an evil wizard’s chest, for example, or in a dusty tome in an ancient library.
While this is not meant to be an exhaustive list, it's strongly suggestive that finding a spell means finding it written down. It certainly doesn't suggest that knowing it is the same as finding it.
The second method for Wizards to add spells to their spellbook is from their prepared spells.
If you lose your spellbook, you can use the same procedure to transcribe the spells that you have prepared into a new spellbook.
You don't prepare your Bard spells, so this method won't work either. Note that even if you did prepare Bard spells:
You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.
So even if you did prepare Bard spells, they wouldn't be considered to be prepared by the Wizard class and wouldn't be usable with Wizard class features, including scribing.
With all that said, you should be able to craft a spell scroll of Comprehend Languages as a Bard (Crafting a Magic Item, DMG pg. 128) and then copy it into your spellbook from there.
A wizard spell on a spell scroll can be copied just as spells in spellbooks can be copied.
However, both the rules on finding spells and the rules on spell scrolls agree that the spell must be a "wizard spell". Unfortunately, the rules never define what it means for a spell to be a wizard spell, or a bard spell, or any other class's spell. The best evidence I can find is this:
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook for free.
The only interpretation I can come up with of this that makes any sense is that wizard spells just means spells on the wizard list. This would mean that spells common to both the can be scribed by a Bard and then copied by a Wizard.
This strategy is reliant on some ambiguous points, and requires explicit DM permission, since it's up to them whether you can craft items or not. There are also additional conditions to copying spell scrolls written in the DMG entry for spell scrolls.
No you cannot transfer spells prepared as a Cleric into your spellbook
Just above the text that you reference, the sidebar in the PHB explains
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.
The fact that the book explicitly says that it contains wizard spells is the killer here. Spells that you prepare as a cleric are not wizard spells. They are cleric spells, even if they are on the same spell list.
We know this because of the rules for multiclass spellcasters (PHB pg. 164)
Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell. Similarly, a spellcasting focus, such as a holy symbol, can be used only for the spells from the class associated with that focus.
From this, we establish that your prepared spells as a cleric are "Cleric Spells" in that they are prepared as a cleric, and cast as a cleric; not as a wizard. And your prepared spells from your spellbook are "wizard spells" for a similar reason. Even if the two appear on the same spell list, each spell you have prepared is associated only with one of your classes.
The PHB then goes onto explain that when copying spells from spellbook to spellbook:
This is just like copying a new spell into your spellbook, but faster and easier, since you understand your own notation and already know how to cast the spell.
If copying from book to book is the same as adding new spells except faster, then we know that you can only transfer over wizard spells since you can only copy new wizard spells into the spellbook.
Finally, As you have pointed out:
you can use the same procedure to transcribe the spells that you have prepared into a new spellbook
The procedure in question is the same as copying over a new spell, or a spell from one book to another. Both of these processes require wizard spells to work. Thus, even though copying a spell down from memory doesn't specifically add any new restriction, it doesn't explicitly lift the general limitation on the procedure; the precondition that the spell in question is a wizard spell.
By RAW? No
The spellbook rules say this:
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: