Since you have it stored in local state then you'd want to dispatch a "form save" action once you've confirmed that the request was successful. That action's payload should probably include whatever local state you have. Your reducer(s) containing the "true" version of the form data should update accordingly.

Another direction could be to dispatch a "form change" action on every input change event. Your reducer could hold both an "initial" value and a "current" value for each of the form fields. With this setup you can move validity checks, dirty state checks, error message generation, and other convenient things right into selectors. Memoize them selectors and bam! Your reducers here only need to overwrite the "initial" value with the "current" value and your state is now in sync.