Yeah I agree. I just suck at caster play so I have a hard time understanding the limitation of spells. Part of the problem is I started the party of with a NO arcane restiction. I told them later I mwould let them multiclass or give them an arcane follower when it seemed appropriate in our low arcane world. He showed up at a session and asked if he could jump in. I asked what he was. He said he was a dwarf with a battle hammer and armor. I assumed that meant a fighter. So even though I knew he was a major min maxor the other martial players arent too shabby so I figured it would be ok. I didnt even know he was a caster until he cast his first spell.... then he just laughed and said he hadnt lied to me.
This is a great learning opportunity for you, I think

.
Lessons:
1) If someone shows up at the table with a character, take a look at it first.
2) If a known min-maxer shows up at the table with a character, take a very hard look at it first.
3) Make it well-known to players that your rules are rules, not wishes. (None of this "I wish he'd create a new character": it's your game, if you tell him to create a new character, that's what he does, or he leaves.) You put a no-arcane limit in effect, and that stands. His sneaky trick is totally irrelevant to the rule.
How to fix this? I'd contact him immediately, reiterate the no-arcane rule, and tell him that he'll need to send you a no-arcane character sheet before next session if he'd like to keep playing. Apologize for the confusion if you want--I would, but it's not necessary.
Or you could be a jerk and enforce the rule he knows about. You said no arcane, so any arcane spells he tries to cast don't work. That's not something I'd do, but it'd be tempting not to remind him about the rule until he tries to cast a spell.