Oh God - I was kidding! Anything someone mails you is yours to do with as you please! I don't think there's anything "wrong" with what you're thinking of doing, except that, unless you're tactful, it could appear a little crass. I'd mention the award to the other schools (and there's no problem naming the figure), but I would't necessarily send it unless they asked!
Good luck, and let us know what happens!