Unlike many other Android apps, you can't print directly from the default Google Messages app. There are some workarounds you can try, however.

You can print text messages from your iPhone in several different ways. There's no Print command in the Messages app, but you can copy messages into an email message and print or save that. You ...

To print text messages from your Android phone, screenshot the message and then go to the share options. Press print and select the printer on the Wi-Fi network you want to use.