Storing messages sent by delegates [Send On Behalf, Send As]

By default, Exchange Online keeps a copy of all messages sent by delegates from a shared mailbox in the Sent Items folder of the user who sends the message. This is insane because it is usually more efficient to have the messages stored in the shared mailbox.

This Cmdlet manage the right properties

 Set-Mailbox –Identity 'sharedmbx' –MessageCopyForSendAsEnabled $True –MessageCopyForSendOnBehalfEnabled $True  

The MessageCopyForSendAsEnabled property is False by default. If set to True , Exchange Online keeps messages sent by delegates as the shared mailbox in the delegate's mailbox and also creates a copy in the shared mailbox. The same about MessageCopyForSendOnBehalfEnabled property.