Iphone account - Register to email

Hi all.

I play L&K in my iphone and I connect directly from the phone with "login ID" and associated in my phone game and "gamecenter"from apple, I dont create the register or email account...

Well, I restore my phone to factory default and after install the L&K, the game generate the NEW "login ID"...
Was necessary I restore my phone backup to back to play in my original "login ID".

My question is: Can I register my email and associate my "login ID" used in my iphone?

Regards,