Spellcasters are a pain to run. You can do a few things:
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Assuming you're playing in person, you can make or buy spell cards and lay them out or put them on a ring.
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Pick 3-4 spells as their "signature" spells and primarily use those, and only deviate (perhaps via option 1) in special circumstances. Single-target, area of effect, buff/debuff/control, and healing are usually good. Also remember you can always re-flavor the spell description on the spot.
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If it's a party ally, turn over control (with the entire list of spells) to a player to control during combat. Provide guidance if they try to perform an action that would stray too far from what the NPC would do.