Citing Anderson County Coroner Greg Shore, Greenville Online reported that Hall died on Saturday afternoon and an autopsy is scheduled in Anderson on Sunday.
In a Facebook post, Hall's brother Gerald Gambrell, said, "God took his strongest soldier. Jacob will be with us forever and always in our hearts. I love you little brother and I can't wait till the day we meet again. Your my hero buddy. I love you so much watch over your family son."
Two children, including Hall and a teacher were shot by a gunman at the elementary school, a spokesman for Anderson County Emergency Management told reporters on Wednesday.
The students were sent to a local trauma centre. One child was taken to Greenville Health System emergency trauma centre by helicopter.
The teacher was also hospitalised. The suspected shooter, a teenager, is in custody.
