The newest beta of Facebook for Android (version 37) allows users to move the app to the SD card somewhat. Only 50MB, which Android Authority believes is the APK file, are moved while the remaining 150MB stay on internal storage. In addition, this division causes the app’s size to increase slightly. It is not known why Facebook went with this rather than relocating the entire app.
If you like this idea, you can grab Facebook v37 from APK mirror. Beta testers should already have the update in the Play Store. Keep in mind that since this is a beta, Facebook reserves the right to remove or change the feature upon final release.