Save data to MySQL from within jquery loaded page

Question

I have created an example of what I am trying to accomplish:

1. I have an index page with a form + input elements (example.php).
2. When submitted I call a php page via jQuery that processes the form data and outputs result in div on index page (proces.php)
3. From within this php process page loaded in the div I have a button that when clicked I want to save $_POST data + other values from that page into MySQL.

I simply just cannot figure out how to "re-use" $_POST data and new values from example.php file and process.php file so I can save it from proces page when clicking button on proces.php page.

This is the example: http://mazey.dk/example.php

When form on index page is submitted the proces.php is called and here all POST data is parsed. This data I want to save when clicking Save button in proces.php file.

I hope someone can guide me in the right direction.

Thanks

***** UPDATE *****

Let me break down the code I have:

On example.php page I have a POST form with an action and a jQuery/AJAX script that prevents form from submitting in a normal way, instead it sends POST to form action URL. Result is then shown inside the with .previews class.

<script>
$(document).ready(function(){ 

    $('.selectform').ajaxForm( {
    target: ".previews",
    //success: function(res) {
        //$( "#currentOrders" ).load(window.location.href + " #currentOrders" );
    //}
    });

});
</script>

<form action="proces.php" class="selectform" method="post">
    <input name="test" type="hidden" value="123">
    <div class="form-group col-md-9">
        <input name="inputtest" type="text">
    </div>
    <div class="form-group col-md-9">
        <div class="">
            <button class="btn btn-primary btn-lg" type="submit"><i aria-hidden="true" class="fa fa-calculator"></i> Calculate</button> <button class="btn btn-default btn-outline btn-lg" type="reset">Reset</button>
        </div>
    </div>
</form>
<div class="col-md-6 col-lg-6 col-xl-6 col-xxl-6">
    <div class="previews"></div>
</div>

Inside proces.php file (that displays in the .previews ) I have a button. This button I want to trigger a "save-action" so when clicked I can save POST values + other variables that will be defined in proces.php into the MySQL DB. I have no problem in handling functionality to MySQL, but I need to figure out how to call POST data + variables upon clicking the button.

Proces.php file:

<input type="submit" name="save" value="SAVE" class="btn btn-lg btn-default">

<?
    print_r($_POST);
    $newTest = "Check";
    $data = 234;
    // TEMPERATURE CONTROLLER
    $controller = explode("|",$_POST[controller]);
    $controllerCostEach = $controller[1];
    $controllerName = $controller[2];
    $controllerCost = $controller[1];
    $qtyController = $controller[0];
    $controllerAssemblyCost = $controller[3];
    $totalControllerAssemblyCost = $controllerAssemblyCost * $qtyController;
    $controllerCost = $qtyController * $controllerCost;

//SUBMIT BUTTON CLICKED
//E.g if(save).clicked{
echo "HERE I can save original $_POST data + other variables from $_POST values from index file and this proces.php file via standard mysqli_query";
//}
//SUBMIT
?>

I hope with this explanation that someone can help me :-)