Can a multiclassed Wizard/Bard scribe a spell scroll for a spell they know as a bard, then copy it into their spellbook (if it's on both spell lists)?

Question

I'm playing a multiclassed wizard 6, bard 1. I know that you can't copy non-wizard spells into your spellbook.

What if I copied one of the 1st-level spells I have access to as a Bard that is also on the wizard spell list? Can I make a scroll out of it and then have that same character copy it into his spellbook, since it's still a spell that a wizard could learn from his level up?

I've seen other questions like this but never for a spell that was both the spell lists of wizard and another class.

PS: I looked at the link you sent but it doesn't answer the question. That one was talking about a spell that wizards are unable to learn and that is not in their spell list. I am talking about spells that bards and wizards share.

Answer 1

Yes, they can scribe a spell scroll of a known bard spell, then copy it into their spellbook if it's on the wizard list as well

Xanathar's Guide to Everything (page 133) lists "Scribing a Spell Scroll" as a possible downtime activity:

Scribing a spell scroll takes an amount of time and money related to the level of the spell the character wants to scribe, as shown in the Spell Scroll Costs table. In addition, the character must have proficiency in the Arcana skill and must provide any material components required for the casting of the spell. Moreover, the character must have the spell prepared, or it must be among the character’s known spells, in order to scribe a scroll of that spell.

And the relevant part of the description of the spell scroll magic item in the Dungeon Master's Guide (page 200) says:

A wizard spell on a spell scroll can be copied just as spells in spellbooks can be copied. When a spell is copied from a spell scroll, the copier must succeed on an Intelligence (Arcana) check with a DC equal to 10 + the spell's level. If the check succeeds, the spell is successfully copied. Whether the check succeeds or fails, the spell scroll is destroyed.

So, seeing as the spell the Bard is choosing to scribe as a spell scroll is on the Wizard spell list, it will be able to be copied to the spellbook. This is, of course, dependent on the PC having the Arcana proficiency (to scribe the scroll) and passing any required checks.