Click on the Permissions tab and locate where it says Display Name at the Bottom.
Here you will need to enter in the person's 'Display Name', not their username. If you do not know their Display Name you can go to the User Manager under the cmadmin menu.
Once there, locate the person and find their Display Name.
Then type the name into the field under the specific module and select the user and click add.
The specified user now can make changes and edits to this module.