Unload the camera in the usual way, but don't seal the tail on the takeup spool.

Put the film roll showing "exposed", and an empty spool, into a changing bag (or take them into a darkroom). Before closing the bag or turning off the lights, put the tail tab from the backing paper into the slot in the empty spool and wind one or two turns to lock the paper on the spool, keeping the space between them short to minimize risk of exposing the end of the actual film.

Now, with lights off or changing bag closed, continue hand winding the backing from the roll to the empty spool. At some point (after 30 cm or so) the end of the actual film will come out of the roll; it will usually curl away from the backing. Capture it and ensure it goes into the roll you're rewinding to, with as little slack as possible. Continue winding film back to the (formerly) empty spool.

A while later (around 75 cm, give or take) you'll come to the point where the film is taped to the paper backing. There will almost always be a little bulge where the film wasn't perfectly matched when you caught the end in the roll; just peel the tape off the backing paper (not off the film), and continue winding (the pressure of the tight roll will reattach the tape, and the film end won't be moved enough from its correct starting point to matter).

When you run out of backing paper, hold the now-full spool tightly, and open the bag or turn on the lights. You can now load the film into your camera as if new, and it will work just as if it had never had this misadventure.

BTW, this technique also works to wind 120 film onto a 620 spool for use in those few Kodak cameras that won't accept even a trimmed 120 spool for supply. For this, you'll need to intentionally wind the unexposed film to a takeup spool, then wind it back using the above technique, but with a 620 spool in place of the original 120 spool.