Adopt linked variables for components in another file

Additive work in Figma: Two Figma files with the same variables. File1 contains elements like buttons, etc., while File2 is empty. Is it possible to copy buttons from File1 into File2 so that the buttons are automatically linked to the variables in File2 (same names and connections, but different color assignments for the primitives)? If the variables in File1 and File2 are identical, can I copy a button with links to variables from File1 into File2, and will the button automatically link to the variables from File2?