My organisation recently started using folders on their Facebook page. The conversations then can be categorized as Inbox, Unread, Follow Up, Done and Spam.
I regula
After investigating this endpoint, I think ?folders is some ancient param before the rework of the messaging from messages in folders to conversations to pages. If I query my page for the spam folder, I never get messages listed, even though I flagged some with spam. And while they are flagged with spam, I do not get those on the conversations query (without folder=spam).
I believe, facebook changed the system into tags on conversations. You can get those like so: [page_id]/conversations?fields=participants,messages{tags,message}&folder=sent.
Note: The marked "no sent tag" is not related to the folder applied (as they dont work). Maybe the tagging on conversations is the reason you get the same result from querying threads at [page_id]?fields=threads{participants,messages{tags,message}} 
So for now I think, one has to get over everthing there to read the inbox. Yet I am a bit sad about not getting flagged spam messages from the graph. I will investigate this a bit further later^^
Call folder=page_done with Page Access Token to retrieve all threads/messages in Done folder of Page inbox.
{page-id}/conversations?folder=page_done
To get Page Access Token
{page-id}?fields=access_token
The documentation might need some updating. But for now, I can query messages in "DONE" via:
/{page-id}/conversations?tags=action:archived