hi, peedah. since whether the prof uses it depends on whether or not he/she thinks it's a good idea, in communicating with him/her about the letter you might as well mention, "i have a sample letter of recommendation that proved helpful to someone else (or, if he/she knows this person, prof x) as he/she wrote a letter on my behalf. would that be useful for you as well?"
this works because you want him/her to use it and you want him/her to be jazzed about doing so. in asking first if it's useful, you won't need to guess those two things and you won't have to worry you've annoyed the person by offering it without asking. an alternative is to simply give it to the person, but then you run the risk of annoying him/her slightly, which virtually guarantees they'll not use the sample. my exp is that people generally are psyched to have a little help in writing letters, and people generally appreciate being asked what you can do to make this easier for them. i think this recommender may just jump on the chance. good luck!
