In Office 365 and Exchange 2013 CU9, this feature is disabled by default.

For emails Sent As the shared mailbox:

set-mailbox <mailbox name> -MessageCopyForSentAsEnabled $True

For emails Sent On Behalf of the shared mailbox:

set-mailbox <mailbox name> -MessageCopyForSendOnBehalfEnabled $True

For messages Sent As the shared mailbox:

set-mailbox <mailbox name> -MessageCopyForSentAsEnabled $False

For emails Sent On Behalf of the shared mailbox:

set-mailbox <mailbox name> -MessageCopyForSendOnBehalfEnabled $False

Quelle