I'm a software developer (but not in cyber security).
There are multiple ways to recover FB (or some other social media messages).
1. Directly from social media archives. Possible only for authorized employees and probably law enforcement (and such) in some serious cases (but I'm not sure about extent of that).
2. From device that was used to make the post, by using apps such as Dr. Fone. Limited capabilities. Digital forensics experts.
3. I would call it "accidental" - like Hawke did, somebody doing a screenshot and sharing with you.
4. If messages were not deleted, just made private, then you can get these by somehow getting access to target account (by hacking, social engineering etc.). Would not recommend that as it is illegal.
I guessed AP2's password (birthdate, what an idiot) and accessed his Gmail account, the conversations were deleted (WW knew that she is married to "computer guy", so she advised AP on what and where to delete), but I managed to get some interesting info from there nevertheless, that uncovered and resulted in more TT. They left a lot of traces despite being careful - cached chat messages, hotel reservations, hotel searches, location searches. She won't make such mistakes again (I haven't found SI at that time yet so was not trained to handle it correctly - "do not reveal your sources", etc).
FB messages aren't public unless you set it. I'm unaware of any methods to access private messages (except by above methods) and I'm sure that if there were any, FB is constantly patching it up (and introducing new bugs too - absolute security doesn't exist).
@DDay#1:
Me: BS, 40; Her: WW, 32
M: 10y, in relationship 15y, 3DD (8,8,6)
Dday#1: Oct, 2016, Dday#2: Jun, 2017
AP#1: COW PA, AP#2: EA/PA 3 months, AP#3: COW PA
Currently (2024): Plain of the Lethal Flatness