When we receive a case from another help desk system, the incoming email address of that system is captured as the "user". This is changed manually (or via email bonding) to the real submitter of the case, which is modified in the user field. This allows us to communicate directly with the user as the email address of the submitting help desk system is not the real user, it is a system email address. When we resolve cases, the user is notified, but the submitting help desk system is not, this is causing cases to be orphaned on the originating system. We need a way to "cc" or send a different notification to an email address (not necessarily the originating email address) at the originating organization so that they can be informed that the case has been resolved. It may be better to do this when the case is closed, not resolved. This could be made possible by creating an additional email field in the organization record that would be used for the close to user workflow to send an additional email to the designated email address.
To get around this, you could set the external helpdesk email as a user in your asm system, then add them as a stakeholder to the call, this should CC that address into the closure email I believe