Of all the treatments mentioned above, I would avoid all that involve heat. Heat is not good for leather, especially old leather. What you need to do, somehow, is to get some elasticity into the 50-year old leather fibers. Neatsfoot oil might do it (it will take a lot of it); the stuff Jon recommends might do it; I don't know. Your success will depend on the actual condition of the leather, which is very difficult to assess in person, and probably impossible from photos.

Your saddle is a Wrights W3SW ("swallow") which was the Wrights version of the Brooks Swallow. I understand Brooks bought out Wrights at some point, but that's not to say Brooks made the Wrights saddles. Same ownership, but not necessarily the same factory. The frame is the same stamping as a Brooks narrow frame, but isn't as well chromed (if at all) and there are no eyelets in the bag loops at the back. And the Brooks nose piece was chromed, whereas Wrights was black. You may find a date stamped under the cantle plate; I have a similar saddle dated 63, and another dated 73.

I would suggest you accept Bob's offer; he collects neat old saddles. If you do try to rejuvenate the leather, I wish you the best of luck. If you fail, and it breaks (which I consider rather likely) I'd be happy to take the remains off your hands.