There are numerous threads on the forum about issues with Verizon Messages if you want to do a search, but basically:
The Message+ Verizon Messages - Windows Desktop application is not compatible with Windows 10 computers. The Windows messaging client for Verizon messages is being temporarily removed to prevent syncing issues and customers are able to utilize the messaging web client as a windows alternative. http://spr.ly/660416SYe The Message+ team is aware and working on a resolution.
From Verizon Messages App
Four weeks later and the desktop PC Messaging app has disappeared from the Download link on top of the Web Client's page. I know messages sent via PC are not showing up on my phone now. The whole PC system needs to be taken down until it all works. I guess this isn't all that high on the priority list because it doesn't consume wireless data.
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Having access to your favorite messaging app is crucial and we are here to help. Please tell us, when was the last time you sync messages? Is your PC software up to date as well as your cell phone?