To be honest mate, you have no clue if she likes you or not. No matter how intuitive and sensitive you are, you cannot guage how much a woman likes you 9/10. You get the flirtatious type who are all over you, but dont fancy you. And the reserved type who really fancy you, but act 100% normal, and can't show it. They're just totally hard to read. I consider myself pretty good at reading emotions, and I'm sensitive, but I've put my foot in it so many times - chased a girl I'm sure likes me, who turns out to just like me as a friend. Similarly, there have been 3 of my friends who I got on with as a mate, and ended up asking me out on dates etc.
But back on point - if she does fancy you, you have a moral dilemma and there is one right way to do it. Find out if she likes you, and don't do anything if she does. Then tell your mate the story, and then go chat up the lady.
If you do nothing, you're not doing justice to yourself. You gotta be selfish in love, and that's for sure. But if you do something, without asking your mate, you're stabbing him in the back - simple as. You have to let him know the candy is yours before you pinch it right from under his nose.
Signature? No! Obsolete! These days it's all about chip and pin!