Often if Plex is pulls in all metadata except for the poster, it’s because they got a takedown request for the artwork and had to remove it (e.g. Once Upon a Time in the West metadata - #12 by dane22). It looks like that’s what’s happening with the movies you highlighted, since if you look at their entries on watch.plex.tv, the poster is missing there as well:
- Dva machři mezi nebem a peklem: https://watch.plex.tv/movie/all-the-way-boys
- Dva misionáři: https://watch.plex.tv/movie/turn-the-other-cheek
- Dva výtečníci: https://watch.plex.tv/movie/crime-busters
- Dvojníci: https://watch.plex.tv/movie/double-trouble-1984-1
They’re available on your old system because Plex was able to grab the poster before the takedown request. You could use something like WebTools-NG (via ExportTools) or Tautulli’s export feature to export the posters and copy them over to your new system, but depending on how many movies are missing posters, it might be easier to just find one somewhere else (e.g. from TMDB) and add it manually.