Sharing tickets with externals to collaborate

Sharing tickets with externals to collaborate

We have tried to find a no-code solution to share tickets with external 3rd parties for collaboration. Let's say our customer opened a ticket for a server problem and we want to "add" the manufacturer of the server for collaboration. 

We tried to forward the mail to their ticket-system, which generates the well-known ticket-system answering loop and the communication is not added to the initial ticket system (Ticked ID in subject is lost that way).

Then we added the mailadress of the 3rd party ticket system to CC and replied with a text. Ticket ID remains in subject, but the system on the 3rd party site does not reply, it generates a new message (id in meta new, told us Zoho support).

Any ideas how to find a solution based on subject ticket id to place as answer on the ticket? No-code or maybe low-code.