NO NO NO.

BUY a NEW DIAMOND RING.
I am sorry but no woman wants to be reminded of her man's past. It is bad enough knowing that your man has been engaged or married before and having to hear about the ex. But even worse to have to wear something that was for her. Everytime she looks at the ring she will not think about you and the love she has for you but rather the other woman and how much you loved her. You want her to look at the ring and think oh my gosh he spent time and effort into picking out this ring for me and it is truely respects US. You need it to respect you and her not you and your ex!
If you TRUELY love the new woman you are with, you will spend even more time picking out her diamond ring. It is not about how much you spend on the ring(if you don't have the $15,000) but it about the moment, the thought, the care, and the love that goes into the ring.
I promise you, she would rather have a diamond that is cheaper but was picked out for her not someone esle. If you give her someone's esle ring you will only be setting yourself up for trouble!
BUY HER A NEW DIAMOND RING!!!!!!!!!!!!!!!!!!!!