I think you should use the letter in your application, but only after you receive permission from the law firm and the person you helped to do so. I think it would make a very positive impression. Lots of people who work for law firms (including myself right now for a year before LS) are paper-pushers who have no real involvement w/ any cases. This would be a tangible (and touching) way to demonstrate how involved you were in the nuts and bolts of a case.
Follow the proper steps to do so, but I say include it.