Whether a mailbox is used by multiple users as a collaborative tool or a communication gateway to customers, retaining a record of emails sent from a shared mailbox remains an important business requirement. In Exchange 2010, there was a way to configure this behavior, but we did not have this feature starting with Exchange 2013.
Our customers have told us that a shared mailbox should keep a copy of emails sent from the mailbox by all members of the mailbox in its own Sent Items folder. We have taken that feedback and decided to make some changes to how sent mails are handled for shared mailboxes.
We are excited to announce that once this feature is enabled for you, 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.
Read more here