You can enable non-editing teachers to assign students to courses as follows:
- Access Administration > Users > Permissions > Define roles.
- Edit the non-editing teacher role and set the capability moodle/role:assign to allow.
- Click the "Save changes" button at the bottom of the page.
- Click the tab "Allow role assignments" at the top of the page.
- Click the checkbox where the non-editing teacher row and the student column intersect.
- Click the "Save changes" button.