On Tuesday, police found Amber Peat’s body hanging in a hedgerow yesterday, near a path close to houses in Westfield Lane.
It was just under a mile from the 13-year-old’s home in Mansfield, Nottinghamshire, where she was last seen on Saturday afternoon.
Amber, who was just 4ft tall, had left the house with no money or mobile phone following an argument about household chores.
Officers have stated that they will not be treating her death as suspicious.
However, minutes after her body was found, a twisted social media user took to Facebook, where they falsely claimed to have murdered her.
He wrote: "Amber won't be found alive.
"I've killed her.
"I'm using a fake account that won't be traced back to me.
"I'm writing this message to gladly tell you all exactly what I've done with Amber.
"After putting her in the boot of my car, I took I drove to a location I won't specify."
The post, which goes on to include details of violent and sexual abuse, is too graphic to include in full.
Dozens of horrified readers who spotted the messages reported them to the police, and officers have now confirmed that they are investigating the heinous hoax.
A spokesman for Nottinghamshire Police said: "We are aware of an offensive Facebook post which was seen yesterday evening by many people supporting our efforts to find missing Amber Peat.
“We would like to let the public know we are robustly investigating and will work hard to bring to justice anyone who publishes such appalling posts to social media.
“We would also like to take this opportunity to thank the tens of thousands of people who shared our Facebook posts in an effort to help us find Amber.”
Our thoughts are with Amber Peat's family at this tragic time.
If there's something troubling you, then get in touch with the Samaritans on08457 90 90 90.