Generating only one uv image

When I unwraped an object new UVs were generated. They were only on one image.
But then I added new geometry to the same object (in edit mode), and when I unwrap again (with everything selected), the newly added geometry isn’t unwraped on the same image. I need the geometry to be unwraped on the one image. How can I achieve that?
Ty for your help.

Also one unrelated thing: is there a way to save png image with alpha transparency? Or do I have to save one additional image only with alpha, and then process it in image editor.

Hummm, added geometry unwraps just fine with the previous object. Try selecting every face then unwrap by selecting Smart UV Project.

I managed to correct the problem by using “Consolidate into one image” in the Image menu.