A new Conversation Export screen under Reporting lets an admin pick a channel and date range and request an export. You get a secure download link when the export is ready, with no need to email support.
Admins can request a copy of conversation history directly from the dashboard and follow its status in one place. The export is prepared in the background, so submitting the request does not produce an immediate download.
The original launch had a shorter date-range limit. A later update lets you select a longer period and splits it into separate exports. Follow the current screen for the applicable limits and expected wait.