If your account has the Conversation Export option turned on in settings you can export a .csv file of your conversation.
You can access the Export option while in a conversation by clicking on the three vertical dots in the upper right hand corner of the conversation window.
Then, click on Export. When you click “Export,” an email will be automatically sent to you. This email will include a .csv attachment of your conversation.
This file will include all messages and events from a conversation timeline, as well as the timestamp, the user, the content of the message, and more.