Father Pfleger says his son had been coping with an illness the past few years.
Simms died Sunday in Florida four days after a surgery.
Father Pfleger adopted Beronti in 1992. He has another son, Lamar, adopted in 1981. He was a foster parent to a third boy, Jarvis Franklin, who was fatally shot in 1998 near Pfleger's St. Sabina Church.