The actress updated her will in 2007, after learning her cancer had spread into her liver.
Redmond's father, Ryan O'Neal, was not named in the document.
The will also stated that Fawcett wanted to "remain at home for as long as possible during any period of illness or incapacity and to die at home."
The actress died June 25 at St. John's Hospital in Santa Monica. She was 62 years old.
Redmond has struggled with both drug and alcohol addictions. He is currently serving time in a Los Angeles jail, on drug-related charges. Once he is released, he will get a monthly allowance from the fund as well as money to buy a home.
Fawcett did not name actress and friend Alana Hamilton Stewart, who filmed much of her documentary, "Farrah's Story."
Lott indicated in a television interview that Fawcett maintained a long-term relationship with O'Neal because of their son. Lott also said he believed O'Neal and Stewart were using the "Charlie's Angels" star for money and fame.