Magento 1.9.2.0: Amazon Pay For Europe (version 3.0.10) return error when checkout

I had an error “Your session has expired. Please sign in again by clicking the Pay with Amazon button.” when I checkout without logging to the shop.
But the request from my customer is that we can still use Amazon Payment account event when not logging to any shops.
The thing is I can use the same account with another shop without logging. There is only one shop request me to do so.
My step:
1. Place an order without logging.
2. Click “Amazon Pay” and logging Amazon Pay account.
3. The page was redirected Amazon Checkout Page and had an error “Your session has expired. Please sign in again by clicking the Pay with Amazon button.
How can I purchase with the Amazon Payment without login to the shops?