Instead, the court decided that the men convicted of having a primary role in the woman's horrific March 19 death in Afghanistan's capital -- a killing that was recorded in a video that resonated around the globe -- will spend up to 20 years in prison, according to the source.
The decision was made in a secret session, the source said.
On March 19, a mob of male attackers beat and kicked 27-year-old Farkhunda before tossing her off a Kabul bridge, setting her body on fire and throwing it into a river. Like many Afghans, Farkhunda used only one name.
In the appellate court's secret session, three men who'd been sentenced to death in May were resentenced to 20 years in prison; the fourth was given a 10-year sentence, the source said.
Additionally, the court overturned the conviction of one of eight people who received 16-year prison sentences in the case, according to the source.
Members of a truth-seeking committee that examined Farkhunda's death will fight against the sentence reductions if they are true, an Afghan parliament member who served on the panel said Thursday.
The lawmaker, Fawzia Koofi, said that the reductions would be an injustice and that she and other panel members would meet with Afghan Supreme Court judges about the matter Saturday.
Killing captured on video
The video of Farkhunda's death shows her standing, with her face covered in blood, surrounded by an angry horde of men. She is pushed and falls over, and her beating continues with feet, rocks and boards. In the last part of the video, her body is engulfed in flames.
Then it was thrown into a river.
Early reports after her death suggested she was mentally ill, but her tearful father, Nadir, told CNN affiliate TOLOnews that she was a religious teacher who taught the Quran to children. He said there was no way his daughter would burn pages of the holy book, which has been cited as the motive for the horrific attack.
Farkhunda's parents said the killing was instigated by a mullah of the Shah-e-Do Shamshera Mosque in the city's center, who had been angered by Farkhunda's accusations that he was distributing false tawiz.
Tawiz are pieces of paper containing verses of the Quran that are sometimes worn as pendants to ward off evil and bring the wearer good luck.
TOLOnews reported that "in order to save his job and life," the mullah reportedly began shouting accusations that Farkhunda had burned the Quran.
Witnesses said a crowd gathered and hauled Farkhunda into a street.
Afghanistan's Ministry of Hajj and Religious Affairs said it found no evidence that Farkhunda burned the Quran.
Twelve people were convicted and sentenced -- the four who received death sentences and the eight who received 16 years -- on May 6. Eighteen others were found not guilty.
On May 19, a judge sentenced 11 police officers to one year in prison for failing to protect Farkhunda.