Multiplayer Inventory - how to prevent cheating?

I think I see the issue.

SwitchAuthority is a switch that will execute Remote if you are a client and Authority if you are a server.

This means if you pressed J in the client window nothing happened because the switch went to authority and not remote.

Do you have a server window and a client window ?

You should press the H when using the client window and the press j when using the server window.