Sending, receiving, and organizing email in Outlook.com
Hello
Once that outlook.com alias is created for your Microsoft account, it can ONLY be added back to your own account, not to someone else's.
Microsoft doesn't allow recycling deleted addresses; hence, if you try to create it as a new account or as a new alias on another account, it will tell you it already exists.
You will need to give your wife a different alias in this case. Sorry.