Police in Georgia identified a suspect using the ID the renter had on file with the platform.
Admirers wrote birthday cards and watched video tributes to Carter, the longest-living U.S. president in history, ahead of his birthday on Sunday.
Scott Hall pleaded guilty to five charges and was sentenced to five years of probation.
The decision follows a judge denying a similar request from Trump's former chief of staff Mark Meadows.
“It’s not going to stop anything that I’m doing," the Fulton County district attorney said.
Hiram, Georgia, police said James Wyatt Nicholas Norton approached Zoey Nicole Messenger for a brief discussion before shooting her and then himself.
The judge previously rejected a similar effort by former Trump White House chief of staff Mark Meadows.
The woman, whose name has not been released, was in her 20s or mid-30s and had come to the U.S. from South Korea over the summer to join the group.
Lawyers Sidney Powell and Kenneth Chesebro had filed demands for a speedy trial, and Fulton County Superior Court Judge Scott McAfee set their trial to begin Oct. 23.
Prosecutors maintain that all the defendants should be tried together, citing efficiency and fairness.