If you can see Backup and Restore or similar in any of the menus, you might be able to transfer all the data to a PC via USB then select the bits you want to transfer to another phone. That may come with some risks to the new device but it's the only way round the problem I can suggest.
Just to clarify, what do you mean by "deactivated"? If it's only been taken off the ability to make or receive calls or texts, it should still be possible to read the historic messages.