To make it easier to create a user with operators functionality only I have updated install module, so it now precreates role, group, and required permission for operators. So admin now only has to create a user and assign correct group to it.

Here is list of permissions operator role should have.

array('module' => 'lhuser',  'function' => 'selfedit'),
array('module' => 'lhchat',  'function' => 'use'),
array('module' => 'lhchat',  'function' => 'singlechatwindow'),
array('module' => 'lhchat',  'function' => 'allowchattabs'),
array('module' => 'lhfront', 'function' => 'use'),
 array('module' => 'lhsystem','function' => 'use'),
array('module' => 'lhchat',  'function' => 'allowblockusers'),
array('module' => 'lhsystem','function' => 'generatejs'),
 array('module' => 'lhchat',  'function' => 'allowtransfer'),
array('module' => 'lhxml',   'function' => '*') 

If you are creating operator role from back office. That's how it should look like: