Make the copy before you need it
Open My List and choose Create backup. Copy the entire text shown in the backup box, including its opening and closing characters. Save it somewhere private that you can reach from the other device.
Merge in the destination browser
Open YeahMovies there, paste the complete text into Restore backup and choose Merge backup. The merge keeps existing saved choices and avoids adding duplicate copies of the same title. Read the result message to confirm what happened.
If the text is rejected
Check that the whole backup was copied and that another app did not add extra formatting. A rejected backup should leave your current list intact. Do not clear that list while trying to repair an incomplete copy.
What the backup leaves out
It does not contain videos, account credentials or a service’s playback history. Checkpoints are the episode positions you saved here. Recently browsed is a separate local convenience, not the record of films you have watched.