In the next step, push the cable clamp at the rear end of the socket (which is white in our example) onto the cable. Now you can connect and screw the newly crimped wires to the socket. Pay close attention to the right colour coding by keeping the colours of the old conductors in mind.
With the two black phases, you need to try out which one goes where. I had first connected them the wrong way around, so the panel turned anticlockwise instead of clockwise. But that problem could be easily fixed.
In the end, you just need to screw the cover back onto the socket.
And that is how easily a cut through power cord can be fixed! Ultimately, my extension cord is now about a metre shorter than it was before. But at least, the rather simple repair can prevent an expensive replacement.