Can I send text messages between two mobile phones without spending money?

Sure！ This is absolutely ok! Let me tell you something:

First of all, you should back up all the short messages of both mobile phones in the memory card. I believe your mobile phone will have this function.

Secondly, the short messages of the two mobile phones are stored in their respective memory cards, and they can be directly transmitted to each other via Bluetooth if it is convenient.

Well, I hope my answer can help you.