How can find out who the fake person is on facebook?

there's some girl on facebook who is telling lots of lie's and even put on her photo's some topless model.so she as loads of guys as friends and makes up some stories that don't make sense.i asked her if she was born in the uk,she said yes but you can tell from her writing that she is not english,also she wants to be a model so i helped her by giving her a number,but she won't do anything.there's is so many other things which i caught her out with.i want to expose her as a lair,but how can i do it???look for yourselves at her pictures,someone might know who it is she says is her.her name is kate gill(bristol uk) and the photos are not just quick snaps,there like proper calender girl shots.