Are you sure there's no trace of the stamp? I thought I saw it on the photos of the left side of the bike. Could be my imagination, of course.
It's hard to say what's the best thing to do with a saddle in this condition. The leather has deteriorated, and you can't know how much strength it has until you exceed its strength and it tears. There is nothing you can do that will rejuvenate it or strengthen it. If it were really hard, you might want to soften it, but it looks fairly soft already so I doubt that's what you want. I presume you're not planning to ride it much, right? And when you do, you'll be wearing normal clothes, not lycra cycling shorts etc? If that's the case, I would definitely not put any of the greasy or waxy stuff that's normally recommended for a leather saddle; it'll just make a mess on your pants. A little bit of neatsfoot oil would do no harm, it'll just get absorbed and disappear, but even so, I doubt it will do much good.
If I were going to ride it, I would cut a piece of firm foam --I'm thinking of the kind of foam used for flotation-- and stuff it between the leather and the top rails. Enough foam that when you sit on it, your weight is transferred directly to the rails, rather than supported by the leather. If you do this, take some time to cut the foam so it doesn't distort the shape of the leather; it should neatly take up all the interior space, but no more. Another way to do the same thing is to take the really thin foam, like the kind of sheet foam that a new electrical appliance (computer monitor, microwave oven, TV) comes wrapped in; and fold it up into a triangle of the right size, and stuff that under the leather. Am I making sense?
