Hello, Mariusz Ch. you messed up a bit, we don't skip anything in the installation!
in the new socket, connect the neutral and protective terminals with a bridge and connect the neutral wire there, the plug is equipped with a cable with five wires in which the wires are connected correctly, i.e. the protective one is the body of the device and the neutral is its "working zero" (control, signaling). A device connected in this way, transferred to any other installation, even with a "differential" will work properly.

Regards.