Once streaming is done, you can easily save live FB videos to your device using Getfvid Facebook video Downloader chrome extension.
Read full content : www.izabo.net/page/faceook-video-downloader
Getfvid doesn't store videos. Neither do we keep copies of downloaded videos. All videos are hosted on Facebook's servers. Also, we don't keep track of the download histories of our users, thus making using Getfvid totally anonymous. When you're downloading files, they are usually saved into whatever folder you have set as your default. Your browser normally sets this folder for you. In browser settings you can change and choose manually the destination folder for your downloded facebook videos.