Problem sending from group email address with Outlook 2010 and Outlook 2003

I've got an Exchange 2003 server and have users with Outlook 2003 and Outlook 2010.  I've got several users who need to send email using the From address of a group.

The users (and a test account) have been setup with SendAs enabled.  When logged onto the test account, I've forced a download of the global address list.  

When I try to send an email with From specified as the group email address specified, I get the error, "You do not have permission to send to this recipient.  For assistance, contact your system administrator".  

I've setup an administrative-level account to do this successfully, but am obviously missing something with user-level accounts.
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Are you sure the problem isn't on the Recipient permissions? Who is allowed to send to this recipient..?
Can GROUP send to that recipient?
Double check 'effective permissions' under the group for one of the users.

The version of Outlook should not matter.

Is your group account mailbox enabled?  If so, use this article on how to enable the "Send as" for your users:

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