How can I backup my text messages from my iPhone 5S to my new iPhone 6S?

It hasn't been included in any iCloud backups, which could be because my 5S is 9.3 iOS, and text messages can only be backed up with iOS 10 or later. But I can't upgrade my 5S to 10, and don't want to either. Are there any apps that can do this process for me instead?

Masukah