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Coming quite late here, still with an important comment.

Thanks to Lars Bergman's solution and explanation (and well done for your crisp analysis, Lars) I eventually understood the puzzle.

Nonetheless, there still remains a big unknown to me : what is the Sun Altitude tagged as "apparent" by Stellarium ? Is it :

- Topocentric ? If so, is it : Upper Limb ? Lower Limb ? Refracted ? Unrefracted ? Refracted Center ? Unrefracted Center ?

- Geocentric ? If so, and by definition, it pertains to Sun unrefracted Center, no questions to be asked here.

From a quick search it would look that the Sun Stellarium height pertains to the Sun center, but the word "apparent" needs to be defined here. And I have not dug out enough - knowing the longitude answer - to check whether it is topocentric or geocentric, refracted or not ...

In other words, some frustration felt on my behalf here simply because the exact Sun height definition was not clearly defined, which prevented me from proceeding any further on firm ground.

And as explained here, the Sun height is an essential data required to solve this kind of puzzle since it is required to derive the Sun LHA, hence the Longitude.

Lesson learnt : Never hesitate to clearly define a problem assuming that your reader is stupid, who I may have shown to be here.

But stupid reader here is still ignoring the exact Sun Height definition given by Stellarium which by the way, he does not use and is not familiar with either.

Kermit