Quick update, this has now been resolved:

Answer we got from Microsoft and what seems to work for us:
Please install December cumulative update for Outlook 2010 from http://support.microsoft.com/KB/2459115

Create registry key to save sent items in shared mailbox.

• HKEY_CURRENT_USER\Software\Microsoft\Office\14.0\O utlook\Preferences
• On the Edit menu, point to New , and then click DWORD Value .
• Type DelegateSentItemsStyle , and then press ENTER.
• Right-click DelegateSentItemsStyle , and then click Modify .
• In the Value data box, type 1 , and then click OK .
• Exit Registry Editor.


Then assign following permission on shared mailbox.

Shared Mailbox - Custom
Shared mailbox Sent items - editor
Add user as delegate and give Editor permission in shared mailbox.