Hello Fergal,
If your Lumia 535 is running on the Windows 10 Mobile operating system, you can back up your text messages by going to Settings > System > Messaging, and turn on Sync messages between devices.
You may learn more about how to back up your stuff on the Windows 10 Mobile operating system by going to this link.
If your phone is running on the Windows Phone 8.1 operating system, we recommend that you use the contacts+message backup app.
Note: As of July 11, 2017, Windows Phone 8.1 users are no longer eligible to receive new security updates, non-security hotfixes, free assisted support options, or online technical content updates from Microsoft for free. Third parties or paid support programs may provide ongoing support, but it is important to recognize that Microsoft support will not publicly provide updates or patches for Windows Phone 8.1.
Even after the end of support, the automatic or manual creation of new device backups for setting and some applications will continue for 3 months, ending October 11, 2017. Other services including photo uploads, restoring a device from an existing device backup and the Store will continue to work for at least another 12 months from the end of support, after which time, services will start to be discontinued.
If you want to learn more about the Windows Phone 8.1 End of Support, please go to this link.
Feel free to reply if you have other questions.