In order to rename an AppScript you much check it out. If it is not checked out, the option to Rename is grayed out. However, if you have more than one AppScript in an Application, then the ability to rename the AppScript is still grayed out.
The administrator wants to copy the Public group from one project to another. Because the Public group already exists in the destination project, he first renames it in the source project (ex: Public_test). He then copies it over.
