While "new" official updates no longer exist, enthusiasts maintain archives of the last stable releases:
: The latest major release is often cited as v8.5.0.0 , which was an AppX package. facebook windows phone xap new
This is the most reliable method for both Windows Phone 8.1 and Windows 10 Mobile. Facebook 8.1 - Download XAP/APPX for Windows Phone While "new" official updates no longer exist, enthusiasts
: Version v11.0.1.0 (XAP/APPX) and v1510.7.114.0 (XAP) are common legacy versions found in archives. facebook windows phone xap new
Installing these files requires "Developer Mode" to be enabled on your device to allow sideloading from external sources. Method 1: PC-Based Deployment (Recommended)