There are too many sites advertising apps that do this, but I know there is a way to manually do it for free. It involves backing up the SMS messages to an XML file. I have done this on the android phone. How do I restore the SMS messages onto the Iphone 6?
Added (1). I originally did a transfer of SMS messages from Iphone to Android using free apps. So I know it must be possible to go the other way.
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Where is a tutorial on how to transfer SMS from Android to Iphone 6, using free apps?