From this screen navigate to Data -> Messages or from the left column, under your device's name, navigate to Backups -> Messages. You should see the Device Overview screen appear. To access text messages on an iPhone, open iExplorer and connect your iPhone to your computer. This tutorial walks through both possibilities. IExplorer can load, read and export text messages that are either on your iPhone or ones that have been saved in an iTunes Backup already on your computer. If you don't want to transfer the entire conversation, you may select each message bubble, or multiples, and click the "Export # Messages" button.
Use the icons at the top of the conversation-view to filter by date-range, show attachments only, or export the whole conversation.
Connect your iPhone or iPad & open iExplorer.Follow these steps to transfer text messages from an iPhone or iPad to your computer: