From LedHed's Wiki
Send Message on behalf of a Distribution Group
This will allow users to send mail as a distribution group thus masking their own email address.
From the Exchange Management Shell:
Add-AdPermission "DISTRIBUTION_GRONP" -user "USER_NAME" -AccessRights extendedright -ExtendedRights "send as"
DISTRIBUTION_GROUP = Name of the Distribution Group you want the user to send as.
USER_NAME = The user you will be granting this privilege to.