Top Law Schools

I'm sure this has been covered already elsewhere, but I just had a recommender send in their letter of rec., after I have already submitted all of my applications. I assigned the letter to all my pending schools, but do I need to alert the admissions offices of each of those schools as well to let them know? Or will my application be shown as having been updated and I needn't worry?

Thanks!

LSAC will automatically update the schools with the new letter.