Forum moderator role
A forum moderator for a particular forum is able to edit or delete forum posts, split discussions and move discussions to other forums.
Role assignment
A user can be made a forum moderator for a particular forum by assigning them the role of teacher in the module context, as follows:
1. Access the forum.
2. Click the "Update this forum" button at the top-right of the page.
3.Access the Assign roles page via the Roles tab (or the "Locally assigned roles" tab in Moodle 1.9 onwards) in the top-middle of the page.
4.Choose the teacher role to assign.
5.Select the user in the potential users list, and use the left-facing arrow button to add them to the existing users list.
Another Method
1. Create a new role, with some (or all) of the forum capabilities enabled. This technique allows a more flexible approach. For example, you can create an account with delete but not editing.
2. Assign the role to the users, for a course, a course category, or even at site or system context, without giving all teacher capabilities.
See also
Showing How to Give a User the Rights to Moderate a Forum]