I don't have a date on when they'll be migrated. There are some technical limitations right now that are preventing it. As soon as those bugs are fixed we should be able to proceed with migrating the messages along with the Message Board Comments as Status Updates.
As for organizing them. You can filter by a user and search all content inside a direct message using the Magnifying glass. This somewhat makes folders obsolete. Private/Direct Messaging is supposed to be minimally used anyway. Online communities are intended to have public discussions and minimize closed door discussions so that as many people as possible are benefitting from responses provided. I don't see much organization ever being added to back to direct messages. Previously there were some organization options for private messages but they went away when they switched to direct messaging, which allowed group messaging and enabled search within private messages. There were probably some other things that happened at the same time but that was years ago now so I can't recall.
Mark
EX Community Admin Team
