Hi Natalie,
We finally found out from where the problem was coming from and fixed it, you'll just have to edit the file "hikashop2.5\administrator\components\com_hikashop\helpers\helper.php" and change these lines :
$shipping_address = $this->app->getUserState(HIKASHOP_COMPONENT.'.billing_address');
if(!empty($shipping_address))
$cartClass->loadAddress($order->cart, $shipping_address, 'object', 'shipping');
By :
$shipping_address = $this->app->getUserState(HIKASHOP_COMPONENT.'.shipping_address');
if(!empty($shipping_address))
$cartClass->loadAddress($order->cart, $shipping_address, 'object', 'shipping');