If you're using an Android then you must open the Verizon Messages+ app and subscribe to the service. There are also lots of apps on the app store that will also let you save them to the phone's SD card.
sprmankalel is correcct, ivans1restoration. There are lots of backup options. The one we recommend to use is Veriozn Cloud. This app allows for a all of your messages to be backed up: http://www.verizonwireless.com/solutions-and-services/verizon-cloud/
What is the make and model of the phone you are using, ivans1restoration?
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