I assume you’re referring to this feature of the School of Scribes:
If necessary, you can replace the book over the course of a short rest by using your Wizardly Quill to write arcane sigils in a blank book or a magic spellbook to which you’re attuned. At the end of the rest, your spellbook’s consciousness is summoned into the new book, which the consciousness transforms into your spellbook, along with all its spells. If the previous book still existed somewhere, all the spells vanish from its pages.
That definitely makes it sound like Wall of Force will be copied over to the new spellbook, even though you still can’t cast it.
You’ll need to be attuned to the Grimoire at the time of switching spellbooks but, apart from that, there is nothing that would stop it from working.
Note that you wouldn’t be able to copy the spell yourself, if you didn’t have the Awakened Spellbook do it for you, if you were not of the the correct caster level.