How to convert a GIF to video?

I found this absolutely stunning GIF that I’m dying to sync up with an MP3 track—but now I’ve hit a bit of a wall regarding the export process.
I actually tried converting the GIF into an AVI file first, but the resulting video is only about one second long—which is a real problem, given that I need the final product to run for at least three minutes.
Does anyone out there happen to know the right way to export this properly?

The GIF is actually stuck in what we call a "loop," which means it just keeps cycling through, making it look like the snow is falling endlessly... I really hope you aren't trying to edit an AVI file right now, because honestly, the easiest way to handle this would be to just go into whatever media player you're using to watch it and toggle the "loop (repeat) playback" setting.

Let me try to clarify my situation, just so we're on the same page.
I have an MP3 file that's about three minutes long—nothing crazy—and I’m looking to merge that audio with a GIF to create a video file (either AVI or MP4, honestly, I don't have a strong preference)
My ultimate goal is to upload that finished video directly to my Facebook wall so my friends can actually watch it rather than just seeing a static image.
Does anyone have any clever ideas on how I might pull this off?

You can convert that GIF into an AVI using the default settings right here: https://cloudconvert.com/

First, grab a copy of FFmpeg from this link: http://fixounet.free.fr/avidemux/download.html

Once you have it, just load up the AVI you converted and use Ctrl-C and Ctrl-V on your keyboard repeatedly until you've looped enough footage to hit that three-minute mark, shall we?

From there, head over to the audio settings and select the track option, make sure Track 1 is checked, then use the dropdown menu next to it to select "add audio track" so you can locate your specific audio file.

On the main interface, you should see that both the Video and Audio Output are set to "copy," while the Output Format is set to "FFmpeg"; then all you have to do is go to "File/save," give your new video a name, and let it run its course... and there you have it.

If you happen to have iMovie installed, you might find it a bit more intuitive to try working with that instead.

Here’s a video tutorial for you

No matter which editing software you happen to be using, the core principle remains exactly the same.

Much appreciated