Unfortunately, there is no way for you to retain a component's changed state after you switch to another screen. It's just how it works. Every time you load a different screen, all the components on it will be reset to the state that they were originally exported as on that screen.
With the way prototypes work, they don't retain or collect any data from the user. They are pretty much a bunch of images, but don't have any dynamic functionality behind them. There is no "database" to store the state of the component. It just works for the current screen, and that's it. There are a few feature requests on uservoice about conditional logic, but I think that's quite far on the dev team's roadmap.
For now, the only way to achieve what you want would be by using a different artboard, where the checkboxes are selected by default, and link to that after the second screen. Ofcourse, covering all the cases of what's checked and what isn't might not be practical.
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