Ok I understand this is my fault.
Still naive after all those years
I thought that if Buffalo sells a 10 meters cable (I paid over $100 for the cable) (even exist 20 meters) to adapt to an out Buffalo outdoor antenna (Another over$100) and I paid again a $15 shipping for the $8 adapter we need to connect to the Buffalo router, I thought that it was to extend the range.
In fact it was for only to "be unable to see much difference in the range'' and only to extend Buffalo sales