Extracting iPhone chat history to be used by Messages desktop app

My iPhone has a perfect copy of my iMessages chat history. I wish the same for my Mac. The desktop Messages app does not have the functionality to import chat history nor synchronise iPhone chat history.

I know there are third party app that allows you to extract specific data from iPhone including Messages chat history. I am not interested in just extracting for backup purpose but to make Messages app read the extracted chat history. In that way it will have the up to date data of my iMessages chat history from iPhone. So it will be synchronised in that fashion.

Is it possible? I know the nature of the chat history file are typically organised in a database file. It should in theory work unless there needs to be some file conversion from the iPhone chat history to make it readable for the desktop Messages app.