If you would like your TeamRaiser admins to also be able to Configure Delivery Groups to add non-TeamRaiser groups to coaching email, you will also need to edit the permissions to include the "Email Management" > "Send but not Edit Email" permission level.

Please note that this will also give the admin access to the Email module in Luminate Online. As such, you may also consider having another admin with the appropriate permission levels Configure the Delivery Groups as your TeamRaiser admins will still be able to select pre-configured groups as part of sending a coaching email with the "TeamRaiser Management" > "Register, Manage and Email Participants and Manage Companies" permission.