You can export a conversation with a contact to view the complete conversation history as a CSV file. Each conversation history includes the inbound and outbound messages, the user details, and timestamps of each message.
Note: If you are unable to export a conversation, ask your org admin to enable the conversation export feature.
To export a conversation:
Go to your Inbox and open a conversation.
Click the three dot Conversations Options menu, then select Export.
The conversation is exported to your email as a CSV file.