Zammad tries at any cost to ensure you’re not sending to groups (so “Zammad sending to itself”).
The only (and in my opinion even better) way would be to assign the other group to the ticket.
This can be done with creation right only, without your agents being able to see the other tickets (or being assigned if they don’t have full rights).
Right now it’s not possible to be agent and customer of other groups at the moment.
This is a feature request already, you can find (and if wanted support) it here: