I found to disable prestashop token, but item is not in cart the first time user submit form. I have json return reponse but not cart update.
{"products":[],"discounts":[],"shippingCost":"0,00 \u20ac","shippingCostFloat":0,"wrappingCost":"0,00 \u20ac","nbTotalProducts":0,"total":"0,00 \u20ac","productTotal":"0,00 \u20ac","freeShipping":"0,00 \u20ac","freeShippingFloat":0,"free_ship":true,"isVirtualCart":false,"hasError":false,"crossSelling":""}