Copy before you change devices
Open My List and choose Create backup. Copy the entire text from the backup box and keep it somewhere separate from the browser you are about to change. The text contains title identifiers and episode checkpoints, not videos.
Merge in the other browser
Open My List there, paste the complete backup into Restore backup and choose Merge backup. Supported saved titles are added without creating duplicates. Existing episode checkpoints in the destination browser stay in place rather than being replaced silently.
If the text is rejected
Check that you copied both the beginning and end. A partial selection is not a complete backup. Very old or unrelated backups may use an unsupported format, and titles no longer present in the catalog may be skipped. Read the result message after merging.
Do this before clearing site data. Once a browser's local list is removed, another device cannot reconstruct it unless you kept a copy.