Zoho desk integration with third party helpdesk system

Zoho desk integration with third party helpdesk system

I have the following question and would need some advice:

* We currently use a shared inbox in exchange 2016 (itsupport@)
* We have two extra (external helpdesk solutions) 
* We would like to integrate all the helpdesk into one solution.

So  how could we support following scenario:

* User is sending email to our itsupport@mydomain.com address => Creates a ticket in Zoho Desk
* Agent looks at the ticket and sees that it should be solved by external party
* Agent updates the ticket and sends an email to the external parties helpdesk system (Can you send emails out of Zoho desk to a different address ? eg. itsupport@thirdparty.com using for example our internal address itsupport@mydomain.com
* Third party ticket system sends back a ticket reference 
* Third party ticket system sends a notice that ticket has been solved
* Agent sees it and notifies the internal user
* Internal user checks the solution and all good
* Agent closes Zoho desk ticket?

Thanks a lot!