Ok, I added into the circuit a 10k trimmer between R6 and R8 (as it was in the original schematic) and I set the voltage on pin 6 at 4.5V.
I set the output voltage at 11.98-12.00V, and the current to about 1A, and I used a load with a transistor and a light bulb and I slowly increased the current using the pot from the load schematic (the attached schematic, I used a 10k pot). When the current reached 1.05A, the led illuminated and the output voltage started to decrease slowly as I was rotating the 10k pot.
In your opinion, the led notification circuit is Ok ?