Yes, this is possible. Instead of using multiple screens, it would be VERY EASY to do this using virtual screens (Horizontal or Vertical layouts and switching their Visible property from true to false to show or hide them. Here is how
Alternatively you can use a TinyDB. To do what you want is complex. You will have to save the checkbox state in Screen1 , then in the Screen2.Initialize block read the checkbox state from the TinyDB and assign that state to the 'corresponding' checkbox on Screen2. Yuk, but you can do it, by why put up with that complexity.
You probably can create you app Cha on a single screen, make the app to appear to have several screens, and be happier.
Regards,