The Luxinvert is working. The complete burner and glass were missing. These parts are not available and not possible to find. I made a burner myself.
Here are some pictures of the parts that I made. The burner tube is 15mm diameter brass tube, with a petromax 500cp burnerhead and 500cp ceramic nozzle. I also made a spirit cub. The glass diameter was just a little to wide, so I cut off a small piece of the rim, and made a construction to hold the glass.
Great work on that lamp, especially the parts fabrication. The net holder for the glass is inspiring. Tony