As mentioned in one of the comments in an answer below, I tried following this tutorial. So now I have the following:
The ipn.php file:
It's a problem with the + character, it often get wrongly fetched so I made that workaround, and it worked for me.
payment_data = Sat Jun 04 2016 15:11:16 GMT+0200 (CEST)
foreach ($_POST as $key => $value) {
if($key !== "payment_date"){
$req .= '&' . $key . '=' . rawurlencode(html_entity_decode($value, ENT_QUOTES, 'UTF-8'));
}else{
$req .= '&' . $key . '=' . rawurlencode(str_replace(array('GMT '),array('GMT+'),$value));
}}