Okay, so what you want is that when someone from this group creates a pm, the moderators group is automatically added to the recipient list.
There is no built-in feature for that. If you are self-hosted, maybe you can create a trigger/script for the automation feature, or use a webhook.
I don’t know if it can be achieved with automation, I’m not familiar with it.
In both cases, it will require programming.
Maybe there’s a simpler solution, but I don’t see one right now. 