Israel refers to Fernando as 'Fer' and had the letter published on matador.com.
He wrote: "I know it's good for Fer and is a big step up on a sporting level. It was what we all wanted because he felt very down, powerless at being in a club that was more like Atletico with its economic and management problems.
"We will carry Liverpool in our heart, as we do Atletico. They are two of the biggest teams in the world and all I feel towards them is gratitude for all they have done for us.
"Now a part of supporters hate him, [I think over time they will grow to love him again]. The reasons behind the switch are not financial [he went to Liverpool for less money], the reasons are sporting. His objective is to one day become the best player in the world and I believe that can only be achieved if he is surrounded by the best players.
"I hope the dreams of my brother can be achieved, the same ones as when he followed me about as a little boy. At no point have I stopped believing that he can become the Number One."