I realize the importance of saving certain text messages. The date, time, sender and/or receiver of the message can be viewed and printed via your My Verizon account. To retrieve the actual content of the message you will need to obtain a search warrant from you local law enforcement department.
It is not clear which device you have. If you have an Android OS device, there are several applications in the market to assist you with backing up and storing text messages to your SD card. I hope this information is helpful. Please let me know if you have any additional concerns.
Thanks for your contribution to our community forums,
I share the same concern over the messaging on my child's device. However, there is no way to monitor the content remotely on any device. You can log in at My Verizon to see date and time details for each message and/or call, as well as the mobile numbers these are sent to.
Have a great day!