Thank you very much gentlemen,
Following your advice I did as I had already done with the version 2.5 of P3D and everything went perfectly well.
Presently I have reinstalled all my dear Misty Moorings sceneries(copied from my FSX program into my newly created "Misty Moorings addons" folder in P3D V 3.1) and everything is OK.
Finally, the procedure was quite easy, the only very boring and time consuming task (I keep polite...) was to reload all the ORBX program from Flightsim Store to get the latest version and P3D V.3 editions of these scenery packs.
Finally, I am very happy with the quality of the new flight simulator. Better and very steady images, very decent FPS (20-30 constant) on my rather ordinary computer (Intel I7 3770S 3.10 GHz and a very ordinary mid range NVIDIA GPU). What surprise me is that this time it is not necessary to switch for a new (costly) machine to be able to run this program very decently.
One of the new feature that I really appreciate it is the ability to adjust the brightness and picture quality from within the program.