Make a copy before you need it
Open My List in the browser holding your favourites. Choose Create backup, then copy the complete text shown in the output box. Keep it in a private note or document you can retrieve on the new device.
Merge the copy
In the other browser, open My List, paste the text into Restore backup and choose Merge backup. Recognised saved titles are added. Existing checkpoints in that browser are kept instead of being replaced by an older copy.
If something is skipped
An unrecognised title or invalid episode reminder cannot be restored as a valid catalogue entry. The result reports skipped entries. Incomplete or malformed text produces an error rather than silently treating it as a successful restore. Copy the original backup again if its beginning or ending was lost.
What the copy contains
The text stores catalogue title references and manual season and episode values. It is not a movie download, account password or synced playback history. Everyone using the same browser profile shares its local list, so keep separate profiles or backups when separate choices matter.