Note that if the file is saved in app directory, it may not be accessible to you unless your device is rooted
Since Verizon isn't helping you, you may like to explore a third party solution as explained in my answer here
To summarize :
- Download SMS Backup and restore and take a back up of your SMSes.
From the app see "Backed up (time)" and tap view details. It will list SMS Backup. Tap on that to view conversations and all your conversations are listed. From the 3 dots menu against the conversation you want select print conversation and it will be printed as a PDF file with date and time stamps. You can get sent and received SMSes.
- Send the PDF file by mail