After a conversation ends, you can view the transcript in the Agent Widget. These closed conversations remain in the local browser storage for 24 hours. If you must review older chats or use a different browser or machine, you must search for the activity in Dynamics 365 instead.
How to find and view closed conversations in the Agent Widget
In the agent widget, (1) click the Chats button, (2) click on the Closed Conversations banner, and then (3) click on the Conversation you want to review.