Would it be possible for a Multiclass Order of scribes wizard/sorcerer to put sorcerer spells into their spell book [duplicate]

Question

The Multiclassing rules state that you determine the spells you are able to prepare and cast independently, but it does not seem to apply to spells a wizard is able to transcribe into their spellbook.

Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class. If you are a ranger 4/wizard 3, for example, you know three 1st-level ranger spells based on your levels in the ranger class. As 3rd-level wizard, you know three wizard cantrips, and your spellbook contains ten wizard spells, two of which (the two you gained when you reached 3rd level as a wizard) can be 2nd-level spells. If your intelligence is 16, you can prepare six wizard spells from your spellbook.

Learning Spells of 1st Level and Higher. Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook. Each of these spells must be of a level for which you have spell slots, as shown on the Wizard table.

Your Spellbook (p. 114). The spells copied into a spellbook must be of a spell level the wizard can prepare.

For the sake of the question assume both classes are able to cast up to and including 9th level spells.

Answer 1

No, you can only transcribe wizard spells

There are two ways to get spells into your spellbook:

1. By copying them from a written source
2. By writing down prepared spells

Both only work for wizard spells. Lets look at them in more detail:

Written Sources

The sideabar also explains under the section Copying a Spell into the Book:

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. Copying a 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

This makes it clear that for spells you have not prepared, only wizard spells can be written into the book. If you had a scroll of one of your sorcerer spells, that also happens to be a wizard spell, then you could transcribe the scroll (using the normal rules for that process) into your book. But you could not do it for your innate sorcerer spells, without having such a scroll.

Prepared spells

The sidebar Your Spellbook (p. 114 PHB) states in the section Replacing Your Spellbook:

If you lose your spellbook, you can use the same procedure to transcribe the spells that you have prepared into a new spellbook.

So you cannot transcribe any spell you can cast from memory into your spellbook, only spells you have prepared, and only your wizard spells are prepared, your sorcerer spells are instead known.

(Side note: While this is talking about having lost your book, nothing should stop you to transcribe prepared spells to a new book, say a backup book to protect against loss, without first having lost your book. It would make no logical sense that you suddenly gain that ability by losing your book. The section merely provides a typical motivation / situation for wanting to do so.)

The only spells you know as a wizard are your cantrips, and these likewise cannot be written into the book, adding further evidence that only prepared spells can be written in.