The spellbook of the wizard multiclass.

[Falconcry]

So I have a question about how to handle adding spells shared in common by a multiclass wizard into his spellbook. I have a level 4 character with an Artificier / Wizard split. I understand that just because my artificer can prepare the spell I cannot just scribe it into his book even if they appear on both spell lists. Since my wizard is of the Order of Scribes he should have some benefit if the Artificer uses an arcana check to create a scroll that is not an artificer scroll or a wizard scroll just a scroll.

So the question. If my character has spent the money and time to create a scroll in his own words should my wizard side also need to spend cash again to put it in his own words ... again?

Relevant notations from the Scribing your Spellbook section

Copying that spell into your spellbook involves reproducing the basic form of the spell, then deciphering the unique system of notation used by the wizard who wrote it. You must practice the spell until you understand the sounds or gestures required, then transcribe it into your spellbook using your own notation.

For each level of the spell, the process takes 2 hours and costs 50 gp. The cost represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can prepare the spell just like your other spells.

And from the OoS section about the Wizard's Quill

The quill doesn’t require ink. When you write with it, it produces ink in a color of your choice on the writing surface.
The time you must spend to copy a spell into your spellbook equals 2 minutes per spell level if you use the quill for the transcription.

From Xanthazar's Scribing a Scroll section

1st 1 day 25 gp

So if I have spent a day of downtime and 25 gold and only require 2 minutes to copy it into my book an extra 50 gold seems like a lot when it is in my own words already. A level 4 party would have better use of 75 gold and potentially far more as there are a lot of common spells between these classes. Do I pay the scroll tax twice?

[JonBeowulf]

I'd drop the cost of the second copy by at least 50% if I didn't waive it entirely. You're building something specific and should be able to use what you're building. Then again, I'm not your DM.

Also, if your level 4 party is having trouble coming up with 75 gp then either you're adventuring wrong or that world has economic issues. You could Skyrim the next "dungeon" you clear and should make at least that much selling all the random crap you pick up.

[JLandan]

It isn't a question of it being in your own words, it's a question of crafting a magic item and copying a spell into a spellbook. Two totally separate endeavors.

As a DM I would say you must pay the cost for each. You pay the cost to make the scroll (which you still have after copying). Then you pay the cost to copy it into the spellbook, provided it's on the wizard list as well as artificer.

[kingcheesepants]

It isn't a question of it being in your own words, it's a question of crafting a magic item and copying a spell into a spellbook. Two totally separate endeavors.

As a DM I would say you must pay the cost for each. You pay the cost to make the scroll (which you still have after copying). Then you pay the cost to copy it into the spellbook, provided it's on the wizard list as well as artificer.

What makes you think he would still have the scroll after he copies it into the spellbook?

Copying from a Spell Scroll. A wizard spell on a spell scroll can be copied just as spells in spellbooks can be copied. When you copy a spell from a spell scroll, you 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.

By strict RAW he must pay to make the scroll, pay to copy it, and succeed on an arcana check. If said check fails the scroll is lost and he must do it again.

However this is definitely kinda silly, talk to the DM. If I were the DM I'd let you just pay the one cost of writing it into your spellbook no scroll required but if you're going by RAW you gotta pay and then pay again and you still might fail.