Transfer SMS from old to new iPhone

I have a new iPhone, but during initial setup I did not restore from a backup but chose to do a clean setup. Now I want to move my SMS text messages stored in the old iPhone to my new iPhone. I identified the file where the messages are stored (3d0d7e5fb2ce288813306e4d4636395e047a3d28 .mddata) but replacing it in a backup of the new iPhone and then restoring doesn't help (restore error).

How can I manage to have my old messages on my new iPhone? Any help to the above or a software tool somewhere?? (there are many to backup but here it is to also transfer!)