Is it possible to track the source of traffic if the user must switch to a third-party service during registration?

Question

Google Analytics

I need to solve a standard web analytics problem: see which channels and which traffic sources generate the most conversions per registration. But there is a difficulty: when registering, the user must go to another domain. More precisely, it is automatically transferred to another domain, from where, after successful registration, it is also automatically redirected back.
How can you solve the task of analytics of the most effective traffic in such a situation?

Answer 1

I'm not sure about Lesha Fedoseev's answer - most likely the session will break and a new one will begin. Because we left the site :)
If you have access to all domains, then you can set up cross-domain tracking in GA - then the session will pass through all domains and everything will be ok.

Answer 2

I don't see a problem. After returning to the site, the visitor will have a session opened. Since the return to the site will be a referral within the same session, GA will not overwrite the true source of the referral. For such cases, this rule was conceived.