When you delete user account from AD and not delete mailbox itself, it is possible to reconnect this mailbox to the other user.
First find in which database this mailbox exists. If you remember only name of the user, you can use -match operator:
First find in which database this mailbox exists. If you remember only name of the user, you can use -match operator:
Get-MailboxDatabase|Get-MailboxStatistics|where {$_.displayname -match "Kowalski"}|fl displayname,mailboxguid
Then you should get MailboxGuid you need.
Next, select or create mail disabled user and point it with connect-mailbox command
Connect-Mailbox MailboxGuidhere -database databasename -user newuser