“But I just found out that it is possible to click the product item as order. In the right corner abouve it is shown that the item went into the shopping-basket. But there is no Option to enter the shopping-basket anymore. That’s strange.”
YES, if you upgrade to Hikashop 4.4 (huge changes), you need to re-config the cart settings via Hikashop configuration page :). Please ask the Hikashop configuration via Hikashop community forum.
