Assign Case Owner from host not Central

We have a requirement for a process stage rule (not on central) to be able to assign the case owner.

The problem is this value doesnt appear to be synced from host > central (only the other way around e.g., if you take ownership of case in central. this relationship is synced to the host via an API call).

So If I set the Case – User (Agent Assigned) on the host, this isn’t updated on Central.

Is there an existing mechanism to perform this action, or do I have to implement a new API or similar to perform this action.

Many Thanks
JonathanFS