Apprentice Wizard can use spells in the spellbook
Stat block spells are in the spellbook
As an introductory statement: all published adventures use the MM as a reference1.
Most monsters are referred to in bold text: that means "go to the MM and see what that monster has." All other monsters will be in the Appendix for the adventure; each published adventure I have indicates which are in an appendix.
With that in mind, the Monster Manual (page 10, under "Spellcasting") says:
The monster has a list of spells known or prepared from a specific
You can change the spells that a monster knows or has prepared, replacing any spell on its spell list with a spell of the same level and from the same class list. If you do so, you might cause the monster to be a greater or lesser threat than suggested by its challenge rating.
In this case, the CR won't change; they are all 1st level spells, and I'll argue that the three in the stat block are the best choices to be prepared when the PCs are encountered.
Apprentice Wizard is not in the MM. It is in Volo's Guide to Monsters. The stat block in this adventure's Appendix (p. 194) is identical to the one in Volo's Guide (p. 209).
The spells available to that NPC (a first level caster) are (1) those from the stat block, which are all in the spell book:
burning hands, shield, disguise self
and (2) some other spells
false life, unseen servant, witch bolt are the other three spells listed in the spellbook under the "Treasure" section for the encounter; he carries the book in his satchel (p. 29)
He has the stat block spells prepared by default. Makes perfect sense, each is a useful spell: Burning hands, Shield, Disguise Self. Going with that makes it easier on the DM.
Replace one or all of the ones prepared (per stat block) with spells from the book that is available to that NPC wizard. Put another way, this is an NPC wizard with a little "fleshing out" already done for the DM.
- My brother and I both do the same thing in our campaign. For Mage
and Apprentice wizard NPC's, we usually create a spell book and roll
randomly to see which ones are prepared that day before the session
starts. (Some old school habits die hard)
Which do you prefer: simple or tailored? Go with that.
The published adventure does not limit you to the ones in the stat block.
1 On page 7 of that adventure is a section entitled "running the adventure" which states that you need the Player's Handbook, the Dungeon Master's Guide, and the Monster Manual to run this adventure. These are core rule books for the adventure. (SCAG is "helpful, but not necessary," they say).