Hi there, @user12867 
I see that you’ve already had a chat with my colleague Mike from the Support Team. As he said, we do not have a public API that would allow seamlessly integrating any of our widgets. I am really sorry!
However, we agree that it would be a great enhancement, and I’ve added this idea to the Wishlist - Send submissions to CRM via API.
If more users support this request, it might be considered in the future 