Yes, since you said that you're two people, then what you begin with is exactly that, right? The session sharing is something you've layered on top, with extra software, not something you basically get from a VPS+UNIX users, right?

The times I've shared contexts in such ways, then you want to share a read-only view, still with the other user not being able to add more messages, I guess you're really talking about group chats here?