How to recover messages on new phone
How to get messages from old iPhone to new iPhone
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Try one of the options in this document if you are setting up a new iPhone --> Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
If you have pretty much set up the phone then make sure your iCloud settings are set to sync items from iCloud. Of course you also have to have been using this feature on the old phone too.