You send an email from a shared mailbox in Outlook and the sent email does not show up in the sent folder of the Shared Mailbox but it does show up in your sent folder. I tested this with the portal and it seems to work correctly through the portal.
- Login to the Office 365 admin portal
- Expand Groups and Select the Shared mailboxes
- Select the necessary shared mailbox
- Under Sent items, click on edit
- Enable the first option (copy items sent as this mailbox)