Make the backup while your list is still present
Open My List in the original browser. Choose Create backup and copy the complete text. Keep that copy somewhere you can reach from the next device. A screenshot of a few posters is not the restore format.
Merge it into the new browser
Open the same Solarmoviez site, paste the text in Restore backup and choose Merge backup. The result reports added titles, added checkpoints and skipped entries. Existing checkpoints are kept, so an older backup does not silently replace a newer note.
Read an error before changing the text
The restore control expects the Solarmoviez format and recognised catalog entries. Missing braces, unrelated backup formats or invented episode numbers will not produce a useful list. Return to the original complete copy rather than editing title IDs by hand.
Keep expectations local
This transfers supported saved choices. It does not transfer another streaming service’s account, downloaded episodes or partial-video resume position. After restoring, open one saved show and confirm its checkpoint before clearing the original browser’s data.