you can't copy vista from one computer to another, but if the other laptop came with either a recovery CD or a way to create one you might be able to use that, only way to know for sure though is try it.
I assume you have a windows COA sticker on the bottom of the laptop with the windows license key on it? if you do then see if you can borrow a vista CD from anywhere, as long as it's the same version as written on the sticker and you use the key from the sticker it's perfectly legal to install from a borrowed CD.