Can I do “back conversion” of a B&W JPEG to color?

If this image were RAW, the color would still be there. But since it is JPEG, I’m afraid not. The fact that the image is in RGB format does not help, because I’d you look, you will find that in fact for each pixel, each of these values is set to the same thing: (0,0,0), (37,37,37), (221,221,221), or whatever. That is, they’re all gray levels, just represented in RGB triplets.

When the image was converted to back and white, all colors were mapped to single gray levels, and the original color information indeed irreversibly lost.

You could convert the image to true grayscale JPEG, and I think pretty much any program would be able to render that (although some weird devices may only understand the much more common RGB). This will save some space, but since JPEG is compressed anyway, not as much as you might think. And of course this won’t help your reversal wish.

Your only options here are to find the original, or to paint in false color (as if you are desecrating an old movie).