Have you looked at any Backup apps? It sounds like you are talking about doing a straight transfer from one device to the other, which seems curious that they wouldn't transfer especially form the same brand of device to the next version of the same device, but perhaps a backup app could do it. I often recommend MyBackup Pro for these one off things. It used to come with a trial period that included all of the features, bells and whistles. It offered a lot of detailed options where you could pick and choose sometimes very specific items including individual messages and message threads. I'm sure there are others out there if you look around.