Hello ​@arikp ,
Currently, the only way to do this is by accessing the live chat and reviewing each conversation individually. There is no general report that includes all conversations, and I'm not aware of any plugin that provides this functionality.
If you're looking to export these conversations, the closest option would be to create a flow that saves them to a database or a spreadsheet. However, there would be some limitations, as automations are paused when a human agent gets involved, and there is no trigger to capture messages sent by the agent.