How do I upgrade a WoW account to Burning Crusade?

Okay, I have installed and played BC on my computer. I have also installed it on my brothers PC, and he just paid for an account via WoW website..

He's been playing BC, but not with a BC account. How do I upgrade his account? Should he pay for it on the website too? How about buying a new BC game and just use the serial code in it?

quicker to just log into his account and click the link for BC. costs the same and you don't have to leave the house.
Level 65 Dwarf Pally Zul'Jin, For the Alliance.