The Copy Request & Response Burp Suite extension adds new context menu entries that can be used to simply copy the request and response from the selected message to the clipboard.

The extension offers the following copy methods in the context menu of selected messages and request / responses:

Known issue: As a workaround for an issue in virtual machines, if the method with the selected response data is chosen, you have to wait 1.5 seconds before you can paste the copied text.