Final Draft exports preformatted HTML, which is bad, and terrible on mobile devices. Read more.
LastDraft is a free tool which solves this problem. It turns your scripts into responsive HTML, which works great on all screen sizes. If you don't use Final Draft, any other screenwriting software that can export .fdx files should work fine too.
Your script isn't stored or sent to any third parties. Let me know if you see any bugs or room for improvement.