Conversations are only stored if the 'Conversation State Archiving' is enabled under Server-->Archiving-->Archiving Settings in your Openfire Admin Console, and 'Message Archiving' is enabled for either 'Archive one-to-one chats' and/or 'Archive group chats'. Thereafter, the messages are stored in the MySQL database table 'ofMessageArchive'.
This table contains an incrementally updated 'conversationID', UNIX timestamp, and JIDs of conversation participants.
Hope this helps!