How to Delegate Management of Distribution Group Membership to a User

To use the Exchange Management Shell to delegate management of distribution group membership to a user 

Run the following command:

Add-ADPermission -Identity <name of distribution group> -User <name of user> -AccessRights WriteProperty -Properties "Member" 

For example, to grant Demetria the right to add members to the Enteprise Web Services Department distribution group, run the following command:

Add-ADPermission -Identity "Enterprise Web Services" -User "Demetria" -AccessRights WriteProperty -Properties "Member"