To allow a user to be able to send on behalf of a distribution group, simply follow the below:
1) Logon to your Exchange 2007/2010 server
2) Open the ‘Exchange Management Shell’
3) Type the below in, but change ‘GroupName’ to the name of the group and ‘UserName’ to the name of the user you wish to grant these permissions to:
Set-DistributionGroup GroupName -GrantSendOnBehalfTo UserName
4) Press ‘Enter’
That’s it, that user can now select that group in the ‘From’ field in Outlook and send emails as if they were from the email address attached to that group.