Create a copy you control
Open Watchlist and choose Create backup. Copy the complete text into a note or document. It contains recognized title references and the episode checkpoints you saved. It does not include a film file, login details or a streaming subscription.
Move it without replacing existing progress
In the other browser, open the same Watchlist page, paste the text into Restore backup and choose Merge backup. The result tells you how many titles and checkpoints were added. Existing checkpoints are kept, and unknown or invalid entries are skipped rather than turned into invented catalog titles.
Use backups before clearing browser data
A local list can be lost when site data is removed or a browser profile changes. Private browsing may also discard it when the session ends. Keep a recent backup if your shortlist matters to you. After a merge, open a saved series to confirm its checkpoint before relying on it later.