Waze forum

It would come in handy if the chat messages you can send would be kept in a "chat history".
When you're driving and a chat message pops up, you aren't always in the ability to answer. So if you would be able to recall these messages at a later moment in time, that would a lot safer and easier.

Map chats will not, but private messages will. Unfortunately, current functionality doesn't let you reply later from your Inbox.