Can the mobile phone print a short message list?

Absolutely not, the mobile company will not accept this business. The content of short messages can only be extracted by the background management of the mobile technology department through technical means, not to mention the business hall. Even the internal staff of the mobile customer service center can't see it. They can only see the time and number of messages you send each month, who you send them to and from whom you receive them, and the contents are confidential. Only law enforcement departments such as public security organs can communicate with mobile companies for investigation. There is a way, if your mobile phone can be connected to the computer, there is one.