I'm assuming the exuser has been disabled and the mailbox still exists.
Who needs access to past mail, and for how long? What is the business requirement driving this?
Who needs access to mails sent to the exuser's smtp address and for how long? What are the business requirements?
The answer to these two will determine exactly what form your solution will take.
When a user is disabled, the mailbox still exists. If you add self to the associated external account of the mailbox (2003 example), then it is essentially a resource mailbox. You can give others access to its contents and the ability to send as or send on behalf of.
Alternately, you can create a public folder and move all the content from the exuser's mailbox to the public folder. You can set permissions on the public folder to allow access by specific individuals or groups. You can also set age limits on public folders so that the content will be removed after a specified period of time.
If you leave the exuser's smtp address on the disabled account, mail will be delivered to the exuser's mailbox.
If you remove the smtp address from the exuser's account and place it on a public folder, distribution group, or another user's mailbox (manager for instance) mail will be delivered to the object that has the smtp address. If you place the smtp address on a distribution group that has no members, the mail will disappear silently.
Now, let's look at scenario 1:
Bob was a subprime mortgage broker for Acme coprporation, and has moved on to greener in a sales postion at a used car dealership. His mailbox contains important customer contacts and emails with current and former customers as well as potential future customers which his manager Jane, and the rest of his team, Carl and Alice, need to access to maintain ongoing business. Jane wants Carl and Alice to be able to access Bobs contacts folder. In addition, Jane wants access to Bobs entire mailbox and all future mails sent to Bob to go to her so that she may screen them and then assign and forward to Carl or Alice if action is required.
In this case, disable Bob, add self to Bob's account, remove Bob's smtp address and give it to Jane, grant jane full control access to Bob's mailbox, and grant both Carl and Alice access to Bobs contacts. THe mailbox would be used less and less over time, so leaving it where it is is no big deal.
Now take a look at scenario 2.
At diversified widgets, all employees have a mailbox. THe company policy for departed employeees is that:
Their account will be disabled on termination of employment.
Their mail will be retained for 6 months.
All mail destined to the exemployee will be sent to their manager.
Create a public folder for the user, and move the content of their mailbox there. Set an age limit of 6 months. Set permissions so that only authorized personnel can access the content. Remove the smtp address from the disabled account and add it to the manager. delete and then purge the mailbox.
Scenario 3:
At consolidated magnesium, the company policy is that upon termination and employee's account and associated mailbox will be removed. Inbound mail will be sent to the bit bucket without NDR.
Easy enough. Delete the user and add the smtp address to a distribution group with no members.
I hope this helps.
