ESP-8266

Hello,

Please, I would like to receive some advice about how to use two ESP-8266 connected to Arduino boards (a Nano and a Mega) to communicate to each oter through the internet.

Is that possible?

Thank you in advance.

Yes.
https://tttapa.github.io/ESP8266/Chap01%20-%20ESP8266.html

Nick_Pyner:
Yes.
A Beginner's Guide to the ESP8266

Hadn't seen this before. Just about everything you need to know about using the ESP8266 with the Arduino IDE.