So you are running Exchange Server 2003?
If you dont want to keep the old account just delete it, then run the mailbox cleanup agent in Exchange System Manager. Now find the mailbox in Exchange System Manager right click and select reconnect and select the new owner of the mailbox.
If you want to keep the old account just right click on it (in ADUC) Exchange Tasks | Delete Mailbox.
Just rember to check that deleted mailbox retention is set (it is by default but it is always good to check). Then follow the last part of my instructions above.
Regards
Ben Hoffman
Microsoft MVP - Windows Server System Exchange