Although you can use iCloud to sync mail, contacts, reminders, notes and other data across devices, the same can't be said for certain kinds of personal data, like texts and multimedia messages. To copy texts from one iPhone to another, you must create a complete backup of your old device using iCloud and then restore all the information from the backup on your new iPhone.

Create a Backup

On your old iPhone, select "Mail, Contacts, Calendars" from the Settings menu and then choose "iCloud" from the Accounts section. Scroll down to and select "Storage & Backup" and confirm "iCloud Backup" is enabled. Touch "Back Up Now." A wireless connection is required.

Restore From Backup

On your new iPhone, follow the on-screen prompts in the iOS Setup Assistant to configure your iPhone and log in to your iCloud account. When you reach the "Set Up Your iPhone" screen, touch "Restore from iCloud Backup" and then choose the backup you just created. The Setup Assistant loads the backup, along with all your data, onto your new iPhone.