Save Sent Items in Shared Mailbox Sent Items folder

Office 365
To enable or disable it in the Office 365 admin portal:

Login into Office 365 Admin portal
Expand Groups and select Shared mailboxes
Double click on the shared mailbox you want to change
shared mailbox settings dialog
Click Edit under Sent items
Change the settings then Save and close the dialog.
enable sent items options



Cmdlet for Exchange 2013 CU9 and Office 365
To enable it for emails Sent As the shared mailbox, set the enable flag to true and run the cmdlet:
set-mailbox mailbox-name -MessageCopyForSentAsEnabled $True

To enable it on all shared mailboxes, use this cmdlet:
Get-Mailbox -ResultSize unlimited -Filter {(RecipientTypeDetails -eq 'SharedMailbox')} | set-mailbox -MessageCopyForSentAsEnabled $True

If the email was Sent On Behalf of the shared mailbox, use
set-mailbox mailbox-name -MessageCopyForSendOnBehalfEnabled $True

To disable it for emails Sent As the shared mailbox, use this cmdlet:
set-mailbox mailbox-name -MessageCopyForSentAsEnabled $False

If the email was Sent On Behalf of the shared mailbox, use
set-mailbox mailbox-name -MessageCopyForSendOnBehalfEnabled $False