When you open the web UI and select PurePaths from the left menu you see a list of PurePaths, selecting one of these will display an area with the top findings to assist with analysis. If you want to see the PurePath tree, you can simply click "Analyze PurePath" -> select the transaction -> click the PurePath tree tab.
You can also configure your web UI to connect to the thick client and once you click Analyze PurePath select the ellipsis at the top right of the screen and click "open in client".
You will need to check the configurations in the client settings. Settings -> Dynatrace Client Preferences -> Services. Ensure that you have enable web services and non-SSL connections checked as needed. If you have a proxy configured you can enter that information here as well. You should then be able to connect to the client from the web.