Do you use iCloud for your iPhone backups? If YES, then you can use that method to restore your new iPhone from. QuickStart also works well and would recommend that you try that first. Yes, your texts will transfer over. If QuickStart method does not work, for any reason, then you can always go back and use the restore from iCloud backup method.
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Transfer Data from old iPhone to new-
Do you have a backup created either on iCloud or on your computer?
Method 1 - Backup your old iPhone on your computer like this 👉 How to back up your iPhone, iPad, and iPod touch - Apple Support and then Restore your new iPhone from that backup like this 👉 Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
Method 2 - The Quick Start method and here is how to do that 👉 Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
Axel F.