This article explains how owners or moderators with the privilege to "Add, remove, and change moderator privileges" can promote a member to moderator.

To promote a member to moderator status:

1. Click Members from the list on the left of any group page. 
2. Locate the member on the "Members" page.
3. Click Edit Membership below the member's profile. 
4. Click Change to Moderator under "Membership Privileges." 
5. Click Make Moderator to confirm.

The moderator you appoint will have basic privileges in the group features you've made available, including Files, Calendar, Polls, Database, and Links. In these areas, the new moderator will be able to add, edit, and delete items, including items submitted by other members.

You also have the option of assigning them advanced moderator privileges for the Messages, Members, and Settings areas.