By default all shared mailboxes will retain a copy of emails sent from the mailbox. You will no longer have to figure out which mailbox member sent an email as the shared mailbox or on behalf of it.
In Office 365 and Exchange 2013 CU9, this feature is disabled by default.
Enable the feature
For emails Sent As the shared mailbox:
set-mailbox -MessageCopyForSentAsEnabled $True
For emails Sent On Behalf of the shared mailbox:
set-mailbox -MessageCopyForSendOnBehalfEnabled $True
Disable the feature
For messages Sent As the shared mailbox:
set-mailbox -MessageCopyForSentAsEnabled $False
For emails Sent On Behalf of the shared mailbox:
set-mailbox -MessageCopyForSendOnBehalfEnabled $False