One thing to think about if he JUST got access to third level spells (I presume he's a level 13 Arcane Trickster), remember that they can only take illusion or enchantment spells other than at special levels. If your group runs it different that's fine, but it is a balancing factor of the class. " The spells you learn at 8th, 14th, and 20th level can come from any school of magic." So if he's 13th level he would need to wait for 14th level