OK, there it is. It was the best camouflage trick I have seen. It seems that the said “beast”, an insect as it has six legs… covers itself with debris through some mechanism that I imagine it to be like an insect version of Velcro although it could also be a sticky secretion on its body where the debris gets glued! Nature surprises us all the time with large and small things!!!
I have also discovered that it is very difficult to know what it is as -I am sure- it changes according to the surroundings! However, I will continue looking for it and keep you informed.