the laser stopped emitting light after I tried to engrave on the mirror glass from the reflective side, i.e. not from the side with the paint and silver layer. Is this possible that the laser is damaged? What could be damaged? What needs to be replaced?
I have already spent many hours working with the laser, but I am still a beginner.
LED laser, Sculpfun S1, 5.5W
Yes, very likely you burned the lense and it will need to be replaced.
If it helps, when I am engraving a mirror, I always engrave from the paint side. Note, you will have to “mirror” the output so that words will be facing the right way from the observers POV.
When engraving highly reflective surfaces (like stainless steel tumblers), I turn on the laser at low power and set my media an an angle so that the reflection does not bounce back to the laser source.
Always always always wear your laser safe goggles/glasses.
Thank you very much, it means that I need to replace the lens and not the laser module itself that emits light - this one is ok. So I need a special lens here.
The lense is mounted in your laser head. They get dirty, they need to be cleaned. As far as I know, they are replaceable. It is possible that you did destroy the LED emitter, but check the lense first.
Do you get any light out of the laser when you try to engrave/burn??
Oh, I see that you get no light. The. It sounds like you did burn the laser source. Good news, laser heads are not expensive 
thank you for communication in this difficult moment 
.
Our condolences to the departed lens and family.
I know how I felt when I toasted a lens on the co2… 
At least the 5w units.
I think we’ve all been there 
If there is no light at all emitted, the diode is broken. You need to replace the module as a whole. This has most likely happened. The beam gets reflected back to the source, and the diode is toasted.
If only the lens is damaged, you would still see the light coming out, but unfocused or spread a lot.
That’s why most lasers have a sticker on them Not to point it on reflective surfaces 