I imagine the class which is rising the screen is only prepared for GUI applications, so that's the reason because you can't see the screen in Web UI, is like if you try to call the famous method CL_GUI_FRONTEND_SERVICES=>GUI_DOWNLOAD from the Web UI. Is not prepared for that.
You should investigate if there's any way to pass the user and password via code. I'm not a webservice expert so from here I can't not give you the solution, but I think is good starting point 