Remote diagnoses are always difficult. That’s why my advice is still to always check on site with a building expert.
Window, windowsill (aluminum) and roller shutter box to do
So, the stains are above the windowsill. How is replacing it from aluminum to stone supposed to help? Especially since you really don’t see rising damp now (or in your pictures you only see these small spots).
It’s also unclear what the roller shutter box has to do with the issue, since it itself is plastered and not cantilevered.
There could still be sealing between the window, roller shutter track, and the aluminum board (see orange marked area). But for that, the moisture would also have to rise, or this would have to be detectable.
No matter what one does, it would only be done on one window first or investigated further.