Not sure I fully get your questions. An Elementor form is on your website, right? I do not see how to “send Elementor form through email”. Or am I misunderstanding your use case?
In any case it is not trivial to update an item (client in your case) through a form as forms normally add a new item). You should have something in place that holds the relation to the form data submitted en the existing client. I believe the JotForm app can help out here.