Hi @logoglo,
Thanks for reaching out.
It is not clear what exactly you are trying to do. If you want to assign the Header built using the Cornerstone to a page built with WP Bakery, that is possible. If you want to use the same template on a different page you can Duplicate the page by using any of the Duplicate plugins available in the WordPress repository, which copies the Content, Header andFooter.
If you want to use the Content of any existing page built through the Cornerstone, you can use the Save Template option to save the content as a template and Load Template into another page.
If that is not the case and you are trying to do something else, please explain it a bit more to recognize it.
Thanks