Thanks again, Masonspappy!!! I gave it another try, and found what was going on. The first time after I had exported the .obj I opened it in PoseRay and got some sort of a giant bathtub, which looked weird, so I converted it to .3ds and then back to .obj, and in the end the truss was missing.
So I exported the file again from Blender as .obj, opened it in PoseRay again, and took a closer look. See attached image, what I got. When I imported it into TG, the structure was there too.
OK, now I saw, that everything was there, including the truss, and the extraordinary orbital bathtub. I could easily delete this part in 3ds Max. Still no idea what this is. I hope, that it's no blown up representation of some crucial part, that's now missing, but it looks OK so far.
In some areas this mesh is more detailed than the NASA one, but there are other parts, where NASA is winning. It's probably way more complicated to texture this one, since there is NOTHING set so far, but maybe I'll give it a go.