The classic way of doing this is to use a Pid registry. Elixir comes with the build-in module Registry which can be used to do just this,

You register the process in the registry with a unique identifier for your user. Then it is easy to lookup and if the process is restarted (perhaps being part of the OTP supervision tree) then it can re-register itself. In case of using a pid directly you might end up with a stale pid.

Why do you want to do that? PIDs are only meaningful in Erlang/Elixir programs.

This only works when the servers and the clients are in the same cluster, but the mobile phones should not be connected to the servers’ epmd because the mobile phones are not trusted, right?

The phone shouldn’t be connected to epmd anyway. The phone can send an HTTP request to your Phoenix API which can then return any identifier you fancy – doesn’t have to be the PID itself. You just need a mapping between an ID of some sort (username, email, user’s database ID, whatever) and the PID itself. Registry is one way to do that but honestly, you can just as well keep an Elixir map in a file.

Basically, you need a mapping between some sort of a user ID and the PID of the process responsible for the user.

I understand. There remains a problem though, how to detect a disconnection from a phone? Anyway, the end-of-life of a process should not be on the hand of a phone because it can disconnect at any time without telling the server anything. A heartbeat policy should be fine.