In my experience the in-game window preferences are saved on the local computer (except for the Map, Control Panel, and Personal Informer window positions, which are not saved at all). When you run the game for the first time on any computer you will have to move the windows to your preferred locations and expand them to your preferred size, then they should be remembered from then on.
However my experience with playing AW on different computers is in AWA. I haven't been able to get AWS installed on any of my older computers yet so I'm not sure if it's the same.