Can I use a 13 Pro Max screen on a 14 Pro Max

While I don't have an authoritative answer for you, I am confident of my answer when I tell you that no, you almost certainly won't be able to.

Outside of the SE models, there is almost no compatibility between parts for any given model of iPhone. Each new model has its components specifically designed for that phone and no other. On screens, that means the physical dimensions change, the mounting points, the pinout of the connector(s) as well as the length and positioning of the plug. There are likely electrical changes as well such that even if you could physically plug the screen in, chances are not good that it would even work.

On an older model phone where screens are relatively cheap it might be an interesting experiment to try, but given the almost $400 USD price tag on these screens, I wouldn't care to bet on it.