We understand how important it is to save the contents of an important message, dvmilanese. What Verizon Messages can do is sync messages across multiple devices. While it doesn't allow for the message thread, you can use your printer to print out what's displayed on your computer when viewing the messages online. Here is a link that explains syncing your messages: https://www.verizonwireless.com/support/verizon-messages-faqs/#sync
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