Cmdlet for Exchange 2013 CU9 and Office 365

To enable it for emails Sent As the shared mailbox, set the enable flag to true and run the cmdlet:
set-mailbox mailbox-name -MessageCopyForSentAsEnabled $True

To enable it on all shared mailboxes, use this cmdlet:
Get-Mailbox -ResultSize unlimited -Filter {(RecipientTypeDetails -eq ‘SharedMailbox’)} | set-mailbox -MessageCopyForSentAsEnabled $True

If the email was Sent On Behalf of the shared mailbox, use
set-mailbox mailbox-name -MessageCopyForSendOnBehalfEnabled $True

To disable it for emails Sent As the shared mailbox, use this cmdlet:
set-mailbox mailbox-name -MessageCopyForSentAsEnabled $False

If the email was Sent On Behalf of the shared mailbox, use
set-mailbox mailbox-name -MessageCopyForSendOnBehalfEnabled $False

You can only use use these parameter on shared mailboxes. If you have Send as permissions on a user’s mailbox, you need to use the DelegateSentItemsStyle registry key.

If DelegateSentItemsStyle was added to the registry, delete it as it will prevent the server-side feature from working correctly. Look for it at HKEY_CURRENT_USER\​Software\​Microsoft\​Office\​xx.0\​Outlook\​Preferences or use the registry file for your version of Outlook: