Is there any way I can print out my text messages on Galaxy S4, please?
Yes, there is a way. The first thing to do is to install the application SMS to Text. Once you have installed the application, start it then export the SMS messages as CSV or TXT.
I recommend CSV because you will have the possibility to open the file in Excel. You'll see the SMS messages better and splitted among numbers, contacts, etc.
App page: https://play.google.com/store/apps/details?id=com.smeiti.smstotext&hl=en
You can use a data backup assistant, with it, you are allowed to transfer text messages, contacts, photos, and other data to pc.
how to save text messages.
Transfer the text messages to pc , save them as printable format.
Print out Text Messages from Android Phone .