Reply to an Intercom conversation and assign it to a team or admin via the Conversations API

Steps

1. Retrieve the conversation ID from a webhook event or by searching: POST /conversations/search with filters on contact or timeframe.
2. To reply to a conversation, POST to /conversations/{conversation_id}/reply with a JSON body containing 'message_type': 'comment', 'type': 'admin', 'admin_id': {your_admin_id}, and 'body' (HTML or plain text).
3. To assign the conversation to a team, PUT to /conversations/{conversation_id}/parts with 'type': 'admin', 'assignee_id': the team ID, and 'admin_id': the admin performing the assignment.
4. To assign to a specific admin, use the same endpoint with 'assignee_id' set to the admin's ID — fetch admin IDs via GET /admins.
5. To close a conversation, include 'message_type': 'close' in the reply body rather than a separate close action.
6. Confirm the response contains an updated conversation object with the new 'state' and latest 'conversation_parts' entry reflecting your action.