Two scenarios, two different fixes — depending on whether you've already started using the new phone.
This is the simple case, and JW Library's built-in backup and restore handles it on its own — no third-party tool needed.
.jwlibrary file to your new phone — email, cloud storage, or a cable all work.This is the case that trips people up. If you've already added notes or highlights on the new phone, a straight restore from the old phone will overwrite them — you'd end up with only the old phone's data, not both.
To keep everything from both devices, you need to merge the two backups instead of restoring one over the other:
.jwlibrary files onto one device.Either way, it's worth creating a backup before you do anything else — it costs nothing and gives you a safety net if a transfer doesn't go the way you expect.