Migrating downloads

I need to migrate the downloads from one WordPress website to another.

I have started with installing the same version of DLM and have copied the contents of the uploads/dlm_downloads folder. I have also used the builtin wordpress tools to export/import the download posts.

After that, I can see the download “posts”, but when I open their detail (edit), they don’t include the files themselves – he box below the download description is empty. Also, the File column in the list of downloads is empty too, which is probably the same issue.

What should I do about this? I really need to move those downloads somehow…