Fill a form on one website and second website automatically grabs it
You can do this with a bit of JQuery. Assuming your form action is action1.php which is on site 1 and you have another handler action2.php on site 2:

$('#form_id').submit(function(event){
    event.preventDefault();  // Stop default handling
    var $form = $(this);
    $.ajax({
        type: 'post',
        url: 'action2.php',  // Submit to the second site
        data: $th.serialize(),
        success: function(){
            $th.submit();    // Submit to the first site
        }
    });
});


And now the form will be submitted to both sites and they will both handle it