Delete user account without removing mailbox

Domain runs most Windows Server 2012 and Exchange 2013.

A user account is having problems running a particular program no matter what computer he logs into. I can create a new user account that mimics the user in every way and there is no problem running the program.

So what I want to do is to delete the user account and create a new replacement account. BUT....I do not want to get rid of the email. I want to keep the mailbox and associate it with the replacement user account.

Is this possible? If not, how can I not lose the user's email while creating a new user account for him?

Jonathan