Question:

The merchant would like to use the lightbox for PostFinance Checkout as a pop-up over his webshop during payment.

This is described and displayed as in the screenshot of the doc under point 1:
https://checkout.postfinance.ch/doc/payment/lightbox

At the customer it behaves with the active lightbox (set via the main settings of the module) that when the order is confirmed a redirection to a payment page occurs and there the "pop-up" is displayed on a gray background.

Is the integration just like this, or is there a setting missing here besides the setting in the main settings of the module?

Answer:

The lightbox does not work for PostFinance Card and PostFinance E-Finance.
We need to load these windows in a "Full" window and cannot do this only in the IFrame.

For Credit Card it is a bit different. It works like in the Screenshot.
However, he cannot do this with the all-in-one product of PostFinance Checkout. For that he must have the PostFinance Checkout Flex product.
The reason for this: The all-in-one uses an interface that does not allow us to use the queries in an IFrame (lightbox).