Unfortunately, the concept was premature. Controllers weren’t designed for typing, TV resolutions were lower (720p/1080i), and Facebook was still a desktop-first product.
On your phone, download the Xbox app. You can view your captures and share them to Facebook directly from your phone’s gallery. facebook app for xbox 360 download
Even if you find an old download link or tutorial online, it will no longer work. Facebook on Xbox 360 is a discontinued feature. Unfortunately, the concept was premature