Born in 1930 in Lichtenberg (North West Province), South Africa, during the height of the Great Depression, and suffered in poverty for many years. He attended school in Johannesburg, but in 1947, was unable to continue due to him having to support his parents and 5 siblings. At 16, Ebrahim joined the Passive Resistance Campaign led by Dr. Yusuf Dadoo and Dr. G.M. Naicker. Thousands of woman and men went to jail.

Mr. Moolla became and Executive Member of the Transvaal and South African Indian Congress, and Chair of the Youth Congress, working in close cooperation with the African National Congress Youth League. In 1953, when the Defiance Campaign was launched, Mr. Moolla was in the first batch of defiers under the leadership of Mr. Walter Sisulu and was imprisoned for 2 months.

He became the Assistant Editor and Circulation Manager of Spark, the youth newspaper, later taken over by the African National Congress. On weekends, he sold banned newspapers like The Guardian and Fighting Talk, distributed anti-apartheid flyers and posters, and painted slogans. Mr. Moolla was arrested and beaten by the South African Police on numerous occasions. He was secretary of the Transvaal Consultative Committee and Executive of the National Consultative Committee of the African National Congress, South African Indian Congress, South African Coloured Peoples Congress, South African Congress of Democrats, South African Congress of Trade Unions - which was responsible for organizing the "Congress of the People", and adoption of the Freedom Charter in Klip Town in June 1956.

The adoption of the Freedom Charter leads to the infamous Marathon Treason Trial of 1956 - 1959. Ebrahim was one of the 156 co-conspirators and 156 trialists along with the President Nelson Mandela and others. With the banning of most of the ANC Alliance Leadership, Mr. Moolla was appointed by the Transvaal Indian Congress to replace Mr. Ahmed Kathrada as Chief Volunteer for the Congress of the People.

Mr. Moolla immigrated to Canada in 1974 and worked for the ANC Mission as Secretary and Regional Treasurer. He also worked in most of the campaigns encouraging Canadians to boycott South African goods until the abolishment of apartheid in 1994.