Hi, if you want to change the owner to a client, then you would need to do that on the server, while setting the client as new owner.
As far as I see it, in the “work-good” image you’re setting the server as owner who is already the default owner. In your first “doesn’t work” image you’re setting the client as owner on the client and the server as owner on the server (the event begin play node will be executed by everyone and get player controller with index 0 will return the server on the server and the client on the client).
Imho if you need to change the owner during runtime, then that is a bad sign 
Then it might be easier/better to just do it on the server. So directly where you handle the client input, do a “RunOnServer” and then continue on the server. Then you do not need to change ownership of actors during game play and do not need to switch between server and client execution on the actor.