You are trying to configure the Social Group Sync Add On. You find that the Full Admin cannot:
- See & Configure all rules that are in place
- Create rules for all groups
This is already how the Social Group Sync Add On works, see the configuration guide for details:
- Full Admins can See & Configure all rules.
- They can create rules for all groups, even if they are not owners of those groups
It is just necessary to add the specified user to the correct user group.