Since the official Microsoft Store is non-functional on Windows Phone 8.1 devices (shutting down in late 2022), you cannot download it directly. You must side load via SD card or the Windows Phone Application Deployment tool.
Here are the most reliable sources for the final official XAPs (always scan with antivirus; these are legacy files from third-party archives):
A developer going by the handle XDA_Conan repackaged the last Facebook Beta (v11.4) with updated API endpoints. This is often referred to as the "New Facebook Experience" for WP8.1. facebook windows phone xap new
Features:
Download location: Archive.org (Search: Facebook_Lumia_Refresh_Unsigned.xap) Since the official Microsoft Store is non-functional on
If the official Facebook XAP is too slow, search for third-party XAPs. These are "new" in the sense that the source code was last updated by hobbyists in 2020-2021.
How to find it: Search GitHub for "SlimSocial Windows Phone." You will find a compiled .xap from 2021. This feels "newer" than the official 2016 build because it respects modern screen resolutions. Download location: Archive
Because the keyword "facebook windows phone xap new" implies a desire for longevity, understand this: the community patch is a whack-a-mole game. Every month, Facebook changes a graph endpoint.
To keep your "new" XAP working: