As you know, it has been possible to save all sent items to the Sent Items folder of a shared mailbox instead of the Sent Items folder of the user sending since Exchange 2013 CU9.
Off course, this is also available on Exchange Online but for both (On Premises or Online) you had to use PowerShell to enable this feature on the shared mailbox.
Now, for Exchange Online you can use the Office 365 Administration Portal to enabled/disable this feature. Just logon to your Office 365 Administration Portal – not Exchange Online Control Panel – and browse to Groups\Shares Mailboxes to select the Shared Mailbox you want to manage. The setting will be available in the Property pane
You will also notice you are able to manage Automatic Reply for the Shared Mailbox in the same way
