WS 20: Replacing the battery on a Patek Philippe Ladies' Quartz Nautilus

Opening the "watch case" was easy

Unscrewing 4 screws that were surprisingly lightly fit and then pull a bit on the underside of the bezel - the watch had never been opened before - and the bezel holding the Sapphire was off.
But then I was stalled. I knew that the case back that looks like a screwed case back without notches is actually only dummy on the Nautilus. It sure looks like a case back, but the specialty about the Nautilus watches is that the bezel holding the sapphire crystal is held by 4 special screws on top of the "one piece case".
You can turn the watch and look at that dial from all angles, there is no opening or any other hint of how to get to a setting lever screw or pusher which would release the crown stem and allow you to change the battery.
Since this is a fairly expensive watch and since it had been given to me to change the battery in good trust, I decided to be careful and interrupt my work here. I stopped several times during this project. Against my nature actually, I like to finish projects quickly normally and then enjoy the writing about it. Since this is such an expensive watch and since the Nautilus is one of the most sought after collector's watches still after 35 years of its inception, a bit of patience and coolness seemed appropriate. I left the watch as depicted below in a watch parts holder, covered it and went back to the computer to look for help!

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