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

Unfortunately, a JPEG is a one-way, destructive process. It may be RGB, but it no longer contains the colors originally present, only those written in the B&W conversion process.

If you had the RAW (.CR2) file, however, you could recover the colors. Think of the RAW file as a master, and JPEGs are created from that.

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).

Since you only have a black and white JPG there is no "color" information there. There is only shades of gray, "color" is lost.

There is no 100% automated process to do this for you, you ll have to use a software to perform something like this:

To perform digital colorization, a digitized copy of the best monochrome film print available is needed. Technicians, with the aid of computer software, associate a range of gray levels to each object, and indicate to the computer any movement of the objects within a shot. The software also is capable of sensing variations in the light level from frame to frame and correcting it if necessary. The technician selects a color for each object based on (1) common "memory" colors such as blue sky, white clouds, flesh tones and green grass, and (2) based on any known information about the movie. For example, if there are color publicity photos or props from the movie available to examine, authentic colors may be applied. (3) In the absence of any better information, the technician chooses a color that fits the gray level and that the technician feels is consistent with what a director might have chosen for the scene. The computer software then associates a variation of the basic color with each gray level in the object, while keeping intensity levels the same as in the monochrome original. The software then follows each object from frame to frame, applying the same color until the object leaves the frame. As new objects come into the frame, the technician must associate colors to each new object in the same way as described above.[5] This technique was patented in 1991.[6]

source: https://en.wikipedia.org/wiki/Film_colorization#Digital_colorization

Of course the above quote is for video, but you can get the idea about what you'll expect from a colorization software to use on a photo. Some presets about sky, grass, flesh etc. but mostly you'll have to choose manually a color that "fits", on objects that you'll have to select precisely. A reference colored photo would be helpful.

A quick googling got me this software, which seems to fits your needs (but im pretty sure there are others too)

https://www.youtube.com/watch?v=RNC0JQUevbM