Exchange Online and On Prem save Sent Mails through Send As or Send on Behalf in the Shared Mailbox

By default, if you send a mail on behalf of a Shared Mailbox, the sent item will be saved in the user’s primary mailbox and not the shared mailbox. If you want to change it to expected behaviour, i.e. save the items in the Shared Mailbox, execute following command. This works in Exchange Online and Exchange OnPrem.

set-mailbox -MessageCopyForSentAsEnabled $True

set-mailbox -MessageCopyForSendOnBehalfEnabled $True

References:

https://learn.microsoft.com/en-us/exchange/troubleshoot/user-and-shared-mailboxes/sent-mail-is-not-saved