Michael did not leave Fawaz any of his NZ $198m estate in his will. Michael and Fawaz first met in 2009 and they became lovers.
The 46-year-old also made other unsubstantiated claims. In further tweets he accused the late musician of paying other people to write his music and alleged he "smoked crack" and regularly had escorts over.
He posted: "He never wrote his own music he paid other people to make the music for him and pretended it was him. Not so talented after all."
Fawaz's claims angered fans who called the Tweets "hateful" and "vile".
In August Fawaz was taken into custody with suspicion of criminal damage after he allegedly damaged the house he had lived in with Michael in London's Regent Park.
He was spotted on the residency's roof throwing objects into the neighour's gardens, The Sun reported. According to Police, the damage was "extensive."
The Twitter rant is not the first time Fawaz has publically dissed Michael. In September he called him a "crack head" in a Facebook rant.