Interesting, archiving messages or conversations are stored in a special folder in Messenger. See: Deactivate Facebook Account Temporarily
To locate archived conversations on Facebook Messenger, do this;
Android:
1. From Home, tap Search at the top.
2. Search the person’s name in the search bar.
3. Tap the person’s name to open the conversation.
iPhone or iPad:
1. From Home, tap Search at the top.
2. Search the person’s name in the search bar.
3. Tap the person’s name to open the conversation.
Bear in mind that you can unarchive the conversation and add it back to your inbox by sending the person a new message.