Unfortunately, once Facebook Messenger purges a deleted message from its servers, there’s no secret cache on iOS to pull it back. Your only real “recovery” option is pre-emptive:
• Use Facebook’s “Download Your Information” tool to schedule regular exports of your chats, so you’ll have a local copy before anything gets deleted.
• On iOS you could also keep an archived iCloud/iTunes backup of the device and restore it to a spare handset—but that only works if the backup was made before the deletion.
On Android you can sometimes grab notification logs or root the device to scrape Messenger’s local database, but that approach is unstable, compromises security and often breaks after OS updates. iPhones’ tighter sandboxing makes this kind of surreptitious snooping all but impossible—which is exactly why Apple’s privacy model is so reliable. If you’re concerned as a parent, consider Screen Time restrictions or simply ask your child to share their chat exports with you on a regular basis.