If you have the ability to send as the new mailbox you just added, then in somecases you might also want the emails yousend as to appear in the additional mailbox instead of your own Sent Items folder (the default)
The method to fix this is as follows:
Outlook 2010 SP1 should be installed
Cached mode needs to be enabled for the user’s profile in Outlook
Using Regedit, find the Registry key HKEY_Current_User\Software\Microsoft\Office\14\Outlook\Preferences\
Add a new DWORD registry key called DelegateSentItemsStyle and set it to 1
Close and Save
After that, items sent as a shared mailbox user will in fact be put in that user’s Sent Items If you don’t set Outlook to Cached Mode, the items will stay in the person’s Outbox and never clear, and never show up in the Sent Items.