I need to restore my phone.
How can I make a backup of my text messages on my computer? Is it possible to restore text messages on the new phone?
This is not possible with Windows Phone.
It is a often requested feature and microsoft is reviewing it now. you can vote for this feature on Windows Phone user voice here
This is not yet possible with the windows phone OS. For certain unlocked devices there is a utility called SMS backup which will allow you to do this.
It is possible to backup you SMS on Windows Phone. Here are the steps (Windows Phone 8.1). However, you need a microSD card for this.
You may access this on the phone using Files or any other file management app.
Starting with Windows Phone 8, you can backup text messages to the cloud and restore them on a new phone. You can activate this in Settings > Backup. To learn more about this feature you can visit the help page:
contacts+messages backup app can be used to take a backup of your SMS and contacts.