Three different things you can save
A watchlist entry remembers a title. A backup remembers your list and episode checkpoints. An offline video copy contains media managed by a viewing service. The first two are available here; this website does not supply movie-file downloads.
Check the service before traveling
If you need offline viewing, look for a supported download feature in the destination's app. Its rules can depend on the plan, title, device and country. Downloads may expire or require periodic connectivity. A browser link that opens a movie page is not proof that an offline copy has been stored.
Prepare the exact edition
Confirm the film year, season and episode before downloading within the selected app. Check language tracks too. When time or storage is limited, download only the choices you expect to watch and use the app's own management controls. Do not rely on an untested download minutes before losing your connection.
To move your LetMeWatchThis choices, use list backup. That process needs very little space because it contains references, not video. It does not transfer a subscription, convert a rental into ownership or unlock another service's offline feature.