Sorry for for the delay! New process! :)
(from the original post 1)Select only the 3 internal or external sections

- Big Extrude them one by one with closed faces enabled

- Boolean Merge the upper one (and kill the part not wanted)

- Kill the 3 curves sections

- Boolean Union All

- Kill closed 3 faces sections

- Select all then Shell (internal or external : Normal/ Flip following first choice at the beginning)

Seems fine! :)
Pinky is original
Gold is mine! :)

http://moiscript.weebly.com/uploads/3/9/3/8/3938813/tubeintersection_pilou2.3dm

Hi Pilou, yup I can follow your latest steps. But the Shell function isn't very reliable for thickening surfaces with sharp corners so it can be good to have a different way to do it.

- Michael

All the roads go to Roma! ;) (or almost :)