EE need to know the EID of the new watch. You unpair the old one, pair the new one and it'll give an error because the EID on their system doesn't match. It'll tell you to contact EE with some error code. You can pre-empt this by calling EE and telling them the new EID (it's on the box). They don't care about the IMEI, it's the EID which is important.
I've done this a few times now.
You need to make sure both watches are the same watchOS version otherwise you won't be able to restore and will have to set up as new.
Assuming your current watch is on the latest version of watchOS. If it isn't, then update it.
Unpair the existing watch, that creates a backup on the phone. Make a note of the time you did this so you can select the correct one to restore later.
Phone EE and tell them that you're replacing your watch with a new one and want them to change the EID so it's all good to go. They'll take the number and make the change.
Then once that's done, pair the new watch with your phone. When you get the option to restore from a backup, check and if your latest backup from a few minutes before is there then you're good to go. If it's not listed, back up and set up as a new watch. Don't install any apps, don't set up the wallet, just do a bare install. Upgrade to the most recent watchOS and then unpair it.
Go through the setup again but this time, you should be able to restore the backup you took earlier. You'll know which one it is because you made a note of the time like I said you should.
This sounds more complicated than it actually is. It's pretty straightforward.
