Create the copy
Open My List and choose Create backup. Copy the entire text from its output box, including the opening and closing braces. Store it in your own note or file. It contains title identifiers and saved checkpoints, not downloaded video.
Merge on the other device
Open UpMovies in the destination browser, visit My List and paste the text into Restore backup. Choose Merge backup. New valid titles are added without duplicating the titles already saved. An existing destination checkpoint is kept rather than silently replaced.
If the backup is rejected
Make sure you copied all of it from this site, not an unrelated app. A partial message, an unsupported format or oversized text is rejected. Titles not present in the current catalog may be skipped. Read the result message before deleting your original copy.
Clearing site data can remove saved titles and history. Export before a browser reset, and keep the original browser available until the restored list looks right.