If you're submitting the form using Ajax, simply use getNumber to get the number before sending it. If you're using the standard form POST method, you should use a separate hidden input which you update on submit to send the full international number. Try submitting a valid number below, and then check the 'phone-full' parameter in the URL.
<form>
<input id="phone" type="tel" name="phone">
<input id="hidden" type="hidden" name="phone-full">
<button type="submit">Submit</button>
</form>
$("#phone").intlTelInput({
utilsScript: "../../lib/libphonenumber/build/utils.js" // just for formatting/placeholders etc
});
// update the hidden input on submit
$("form").submit(function() {
$("#hidden").val($("#phone").intlTelInput("getNumber"));
});