Figma usually allows copy-paste between different files - I regularly paste from FigJam to Figma Design, so I don’t imagine it being a lot different with Figma Make.

Are you able to copy and paste into the same file? Try it as a test.
If your can, then try to just copy your content and paste it into the desired destination.

Hope this helps.

I’ve contacted the support for the moment they allow only to copy the code, not the other way around, but i see it as a needed feature since you can use it to generate a specific comp.

Yeah, it creates good designs
It would be super useful if they allow to copy generated designs