Users cannot add existing modules with a Content Manager role.
DNN Evoq 8.5
This functionality is restricted to only the administrator role in the 8.5 environments. Fortunately, in the latest version of Evoq (9.2.2), a user with a Content Manager role has the ability to add existing modules. To have the functionality that you are looking for, you will need to upgrade your environment to version 9.2.2.