Facebook app for Windows Phone 8.1 devices just received an updated to v220.127.116.11. Unfortunately, this is only a minor update with no new features. This update should include few performance improvements and bug fixes, which will hopefully address all the complaints about crashes in the current version.
If you have installed the Windows Phone 8.1 update, this Facebook app allows you to enjoy OS level integrations such as in People Hub, Calendar and Photos app.
The Facebook app for Windows Phone can be updated in the Windows Phone Store here.