I got it!
There were differents problems. I found the clear solution in comments from this post: http://www.digiblog.de/2011/04/android-and-the-download-file-headers/
header("Content-Type: application/octet-stream");
header('Content-Disposition: attachment; filename="test.JPG"');
The important steps: I send everything with a form. The form, to make it work in mobiles, needs to have the target='_top' and the method='get'
It also make errors if the extention (jpg) is not in UPPERCASE and the file name is not between " ".
Now it works in all devices that I try by far. :)
Special thanks to Jörg Wagner, author of the post.