This is almost right, but then the zip file will contain a file 'MANIFEST.MF' instead of 'META-INF/MANIFEST.MF'. I think updateMember will work, though. Also, you need to close FH;

So,

  close FH or die "error writing $file: $!\n";
  $zip->updateMember('META-INF/MANIFEST.MF', $file)
    or die "updateMember";
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