The problem: You have a shared mailbox in your profile and Send as permission on the mailbox. When you send a message from the shared mailbox, the sent message goes into your own Sent Items folder. By default, sent messages are stored in your own mailbox, not the shared mailbox and the DelegateSentItemsStyle registry value is used if you want to store the messages in the shared mailbox Sent Items folder.

If your mailbox is located on Exchange Server 2010, or on Exchange 2013 CU9 or newer (including Office 365 Exchange Online), the Exchange administrator can configure Exchange to save sent items in the shared mailbox automatically. The benefit: you don't need to add DelegateSentItemsStyle to the registry on every computer that uses shared mailboxes, it just works.

Beginning with Exchange 2013 CU9, when a message is sent from a shared mailbox, the sent message can be stored in the sent folder in the shared mailbox without adding DelegateSentItemsStyle to the registry.

Yes, it's been a long time coming, but finally, all shared mailboxes will retain a copy of emails sent from the mailbox. This setting can be enabled or disabled in the Office admin portal or using PowerShell.

Office 365

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

1. Login into Office 365 Admin portal
2. Expand Groups and select Shared mailboxes
3. Double click on the shared mailbox you want to change
   
4. Click Edit at the right of the Sent items row
5. Change the settings then Save and close the dialog.
   

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

You can only use use these parameter on shared mailboxes. If you have Send as permissions on a user's mailbox, you need to use the DelegateSentItemsStyle registry key.

If DelegateSentItemsStyle was added to the registry, delete it as it will prevent the server-side feature from working correctly. Look for it at HKEY_CURRENT_USER\​Software\​Microsoft\​Office\​xx.0\​Outlook\​Preferences or use the registry file for your version of Outlook:
Delete DelegateSentItemsStyle Outlook 2016
Delete DelegateSentItemsStyle Outlook 2013
Delete DelegateSentItemsStyle Outlook 2010

Exchange Server 2010

Update Rollup 4 for Exchange Server 2010 Service Pack 2 introduces the Exchange PowerShell cmdlet, Set-MailboxSentItemsConfiguration , giving the administrator the ability to configure which Sent Items folder a message is copied to. Because this new feature is handled by the Exchange server, Outlook can be configured for Online or Cached Exchange Mode.

However, the Exchange server feature only works if the Outlook DelegateSentItemsStyle registry value is disabled.

To save sent items in the sender's Sent Items folder, use this cmdlet:
Set-MailboxSentItemsConfiguration alias -SendAsItemsCopiedTo Sender -SendOnBehalfOfItemsCopiedTo Sender

To save sent items in the Sent Items folder of both the sender and the shared mailbox, use this cmdlet:
Set-MailboxSentItemsConfiguration alias -SendAsItemsCopiedTo SenderAndFrom -SendOnBehalfOfItemsCopiedTo SenderAndFrom