You can configure Google Analytics Site Search to work with the "full search" part of addwish business Dynamic Search.
Simply follow these steps to set this up in Google Analytics:
When logged into Google Analytics, navigate to: Admin > View > View Settings.
Here you'll have to toggle "Site search Tracking" to ON (if you haven't already done this).
Then specify the keyword used in your search URL's, as the "Query parameter":
Here's an example of how you identify the keyword used in your search URL: