Messages sent from a shared mailbox aren't saved to the Sent Items folder of the shared mailbox in Outlook

Assume that you're using Microsoft Outlook 2010 or a later version, and you've been delegated permission to send email messages as another user or on behalf of another user from a shared mailbox. However, when you send a message as another user or on behalf of the user, the sent message isn't saved to the Sent Items folder of the shared mailbox. Instead, it's saved to the Sent Items folder of your mailbox.

In Microsoft 365, shared mailboxes don't require a license and can't be added to Outlook as an independent mailbox. You can't sign in to a shared mailbox. Instead, you sign in to your own mailbox, and then you open the shared mailbox. When you send or reply to a new message from the shared mailbox, Outlook automatically sends or replies from the sender's account. Therefore, messages are stored in the Sent Items folder of the sender's mailbox.

Cumulative Update 9 for Exchange Server 2013 introduced a new feature that lets administrators configure the Sent Items folder to which a message is copied. For more information, see Exchange Blog - Want more control over Sent Items when using shared mailboxes?

Using Exchange PowerShell, for emails Sent As the shared mailbox, run the following cmdlet:

set-mailbox <mailbox name> -MessageCopyForSentAsEnabled $True

Using Exchange PowerShell, for emails Sent On Behalf of the shared mailbox, run the following cmdlet:

set-mailbox <mailbox name> -MessageCopyForSendOnBehalfEnabled $True