When a user requests full access to a mailbox, you’ll need to run the following via PowerShell:
 
add-mailboxpermission “IDENTITY” -accessRights FullAccess -user “IDENTITY2″
 
Identity = The mailbox being requested access to
Identity2 = The user requesting access to the mailbox.
 
Lastly, the user will need to restart their Outlook client in order to login to the mailbox.