Spell Versatility

Spell Versatility is a Mage skill that is tied to an existing spell slot that the character already owns. After purchasing Spell Versatility, the mage no longer has to memorize a spell to put into that slot and may castspells “on the fly” from any of their spheres that can fill the slot. For example, if a mage has two spheres and a 7th level spell slot they may choose any of those four 7th level spells to cast, so long as the slot is unused; essentially meaning that every spell of that level that they can cast fits into the slot at once. Once a spell has been cast from the slot it is used until the next reset like normal. This skill must be purchased per slot and is considered always functional.

Can a person who doesn't have the spellbook of his second sphere memorise his versatile slot regardless of having the book or not? How does it work exactly for this case. got one book but not the other.