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To properly move one page to another page or site that is using X or Pro theme, you will have to save the page as a template. You can then download/upload the template in the template manager. Once it is imported, you can simply insert the template in the "Layouts" tab when you edit the page.
To know more about the Template Manager, please check this: https://theme.co/apex/forum/t/template-manager/20364
And for more details about the how you can save the page as a template, please check out "Working with Templates" in this article: https://theme.co/apex/forum/t/cornerstone-content-builder-layout/122