I have the same issue. First I thought that it is related to security of facebook groups but it is a different issue. The filename contains an invalid character like ő, ű.
Facebook launches the downloader app which seem to use the MI Browser or something similar to download the file and it fails to catch the filename properly so the download app replaces it with download-xxx.bin. I suspect that the download app has a character encoding issue. It works well with standard ASCII file names.
I couldn't even download it, so I had to do a trick first.
If I copy the link to the MI Browser it will remove the illegal characters from the filename before downloading. This mechanism seems to be broken on the phone so for my case download fails with invalid URL error.
Go to settings, applications, manage applications, MI browser, clear defaults
Now go back to facebook and download the file. Open downloads, select the file, press open, select download here app.
Now you have the downloadfile-28.bin in your directory.
You can open it then with the matching app.
I can only propose a workaround:
Tap on the downloaded file in the notification area which opens the downloaded list (press the check for finished downloads). Tap on the downloaded file. Select copy in the source row. Now open chrome and paste the url. Press enter and save the file. You can find it in the download folder.