Updated.
For simplicity's sake, let's assume he read the book at 16th level, so we just need to add 2 more archmage skill ranks per archmage level (for a total of 10 additonal ranks). Suggestions?
He picked up a bunch more spells, thanks to the headband, tome, and ring of epic wizardry VIII!
Wizard Spells Prepared (4/6/5/5/5/5/4/8*/4/4; save DC 20 + spell level, evocation spells DC 22 + spell level).
0—acid splash, daze, detect magic, read magic;
1st—burning hands, magic missile (x2), shocking grasp, sleep, true strike, 1 more;
2nd—detect thoughts, gust of wind, scorching ray, shatter, web, 2 more;
3rd—displacement, empowered acid arrow, empowered ray of enfeeblement, empowered scorching ray, ray of exhaustion, 1 more;
4th—black tentacles, charm monster, empowered fireball, heightened hideous laughter, heightened stinking cloud, 1 more;
5th—1 sacrificed for spell power, 1 sacrificed for spell-like ability, hold monster, mind fog, quickened true strike, teleport, 1 more;
6th—1 sacrificed for spell-like ability (chain lightning), acid fog, empowered extended ice storm, empowered quickened magic missile, 2 more;
7th—1 sacrificed for arcane reach, empowered freezing sphere, persistent mage armor, persistent shield, 1 more;
8th—1 sacrificed for mastery of elements, extended mage's sword, heightened prismatic spray, quickened wall of fire, 5 more;
9th—1 sacrificed for arcane fire, empowered polar ray, meteor swarm, quickened cone of cold, 1 more;
10th—persistent fire shield, 1 more.