When Facebook introduced the separate Messenger app, with its voracious permission demands, I made myself a mental note not to update my app. Well, that held once or twice, then I thoughtlessly did an “update all” in iTunes and synched. Here is how I got the older version of the app back. I use a Mac. Windows users with a backup if the right age can adapt this method.
In iTunes, I selected the Facebook app in the Apps->All screen and did a “Show in Finder.” Saving that Finder window, I used iTunes to delete the app to the trash. I also deleted it from my phone.
Next, I went into Time Machine* and rolled back until “Facebook 13.0.ipa” was visible. I restored that, then dragged it from the folder to the Desktop. Next, I dragged it from the desktop and dropped it into iTunes, in the same Apps->All window from which I had deleted the current version of the app. Just putting into the proper Apps folder (iTunes>Mobile Applications) through the Finder is not sufficient to register its existence with iTunes.
Finally, I plugged in my phone, went to the Apps window for the phone, scrolled down the list of apps to Facebook, and clicked “Install,” the “Apply” in the lower right. Another sync and I was all set—a Facebook app with the built-in messaging.
* Footnote: Aside from Time Machine, you can probably still find older versions of the app in your Trash. Drag it to your desktop and drop it into iTunes as above.