"Melissa is amazing," Margie Stern, one of the late comedian's closest friends, tells PEOPLE. "I told Melissa, 'Your mother would be so proud of you.' She handled everything. She did everything exactly as her mother would have wanted."
Rivers stopped breathing on Aug. 28 at Yorkville Endoscopy in Manhattan and had to be rushed from the clinic to Mount Sinai Hospital.
Melissa immediately flew to her mother's side, as she was reportedly placed in a medically induced coma.
Melissa also took particular care to make sure her mother spent her final hours in comfort.
"That was hard. But she was in a room with flowers and music. It was fragrant. It was amazing," says Stern, who was at the hospital "all day, every day" with Rivers and Melissa, adding: "Joan looked beautiful at the end."
Rivers died at 81 on Sept. 4. And when it came time to plan her mother's star-studded funeral at New York City's Temple Emanu-El, Melissa made sure every detail was perfect, says Stern.
"I'm in awe of the way she handled everything," she says.