See my answer in your other question here:

https://social.technet.microsoft.com/Forums/office/en-US/a54c7f05-8d19-465b-bddb-de9eb7d45c7e/how-to-inactivate-the-account-and-also-want-to-look-at-previous-email-history-of-user-through?forum=exchangesvradmin

Assuming you've only disabled the AD user and not the mailbox:

You can grant yourself access to their mailbox and add it in Outlook to view the contents.

If you want to export contents to PST, you can use New-MaiboxExportRequest but you may need to enable the account first with a different password. 

If you want to copy particular content from the mailbox into another mailbox then use New-MailboxSearch and Start-MailboxSearch.

Thanks.