You need a version of Facebook that was built for Android 4.2. Generally, Facebook versions ranging from v50.0 to v90.0 are your best bet for Android 4.2 (Jelly Bean). Versions released after 2016/2017 generally dropped support for Jelly Bean.

If you find a compatible version (usually Facebook Lite versions from 2016-2018), follow these steps: Enable Unknown Sources: Settings > Security

To keep using Facebook, you need the – specifically, Facebook version 327.0.0.28.116 (or any variant between 320 and 330).

Because you are installing a file from outside the Play Store, you must enable manual installation:

As the years passed, the original Facebook app became too "heavy" for 4.2.2 devices, which often had limited RAM and processor power. This led to a split in the story: