@pomisingPawns Yes and no it's not that simple though
The 9 years old student of mine reached 2000 at lichess and 1850 at chess com in just one year

How can you coach 1800s when you are only 2000? People should only be coaching others 500 points less or even lower.
Stupid assumption. The O.P. is a certified FIDE trainer, which means that he is able to train everyone but the elite players.
As for your online ratings... well, you can be prowd of them if it pleases you, but actually they aren't worth a penny compared to real FIDE ratings.
i coached a student from about rating 1400 to 1900 but after beating him 27-0 he started using an engine
No you didn't.
I had a 800 cheat against me after I got him from 100-800ish it was I beat him with only two pieces and pawns vs all the pieces he gave up and started trolling

How can you coach 1800s when you are only 2000? People should only be coaching others 500 points less or even lower.
Stupid assumption. The O.P. is a certified FIDE trainer, which means that he is able to train everyone but the elite players.
As for your online ratings... well, you can be prowd of them if it pleases you, but actually they aren't worth a penny compared to real FIDE ratings.
Thank you for the comment. I value Quantum's opinion as well as everyone else's. It's really insightful to hear what people think about chess coaching. To obtain the Fide trainer title, one must have put in a lot of work in the past. Quantum is a good player and he obtained his rating quite easily, according to him. Most of us ordinary people had to put in a lot of work to get there. It would be great to use that knowledge and process to help other students.
As brutal and controversial as it sounds, most people who are not dumb and quite smart and intelligent can easily reach around 1800/2000 with some studying and playing a lot within a few years.