How to send data to the site from a joomla 2.5 modal form behavior.modal?

Question

Joomla

The site has a simple popup form made using behavior.modal. The form is extremely simple, two fields and a Submit button. It should send data from the fields to the mail. If this form is just in the template code, then it works as it should. In the window, clicking on Submit only results in the fields becoming empty.
Here is the code

<?php JHTML::_('behavior.modal', 'a.modal'); ?>
<a class="modal" title="<?php echo JText::_('SELECT'); ?>
                " href="http://joomla2519/templates/lozhki/inex.php"  rel="{handler: 'iframe', size: {x: 650, y: 375}}">
                <?php echo JText::_('SELECT'); ?></a>
Это форма:
<form action="https://joomla2519/templates/lozhki/mail.php" id="callback" class="pop_form">

      <h3>Заказать обратный звонок</h3>

      <input type="text" name="name" placeholder="Ваше имя..." required="required"/>

      <input type="tel" name="phone" placeholder="7XXXXXXXXXX" required="required" pattern="7\d[0-9]{3}\d[0-9]{2}\d[0-9]{2}"/>

      <input class="button" type="submit" />

    </form>

How to deal with it? Joomla 2.5.6