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It sounds like the first file you tried to send was incomplete, as indicated by the “.part” extension. This usually happens if the export process was interrupted or didn’t finish properly. The second file, with the “.wpress” extension, appears to be complete and should be the correct file to send to your friend.
If the export process is fully completed, you should end up with a “.wpress” file. This is the file format that All-in-One WP Migration uses for its backups, and it should contain all the data needed to restore your website on another server.
So, you’re correct in thinking that the second file is likely okay to send to your friend for import.