
Provided that you have created backup through iTunes, you are able to extract the messages on your iPhone to your computer. Usually, you should have one so long as you enabled the automatic backing up service. Since your iPhone cannot be accessed now and iTunes itself cannot help at all, even if you have created iTunes backup file.
So you need third party application which is capable of selectively extracting iPhone messages from iTune backup file, here in this guide, I would recommend iFonebox. As specialized iPhone data recovery software, iFonebox makes recovering lost or deleted messages and extracting existing all the existing messages selectively possible and with ease.
You can download the trial version of iFonebox to have a try at the beginning before you decide to pay for the full version.
Now let me show you how to extract the iPhone messages from iTunes backup file step by step.
Step 1: Install and launch the full version of iFonebox. Choose the recovery mode of “Recover from iTunes Backup”. Then you will be presented with the interface listing all the available iTunes backup files on your computer. Please choose the one for your iPhone.

Step 2: Select the messages to recover by clicking on the icon for messages.

Step 3: Preview all the exported messages and choose whatever you want to recover to your computer. Or you can choose “Only display the deleted items” to show and recover the deleted items only if you prefer.
