Stewart McInroy received a 10-month sentence after sending a series of messages to friends and family of missing Allan Bryant Jnr.
However, McInroy will be out of prison within weeks through automatic early release because the sentence was backdated to April 19, when he was first remanded in custody.
Allan Bryant Snr, who received the messages, said: "He'll be out in a matter of weeks. I don't know what to say - I don't know why they backdated it. I would have been happy with 10 months from now - but he will get time served. To say I am disgusted does not even cover it. It caused heartache beyond words."
The missing man, 24, from Glenrothes, was last seen leaving Styx nightclub in the Fife town last November 3. His family and friends have campaigned to try and find him - staging marches in the town and running a Facebook page titled Find Allan Bryant Jr, which has more than 9,000 followers.
In April McInroy used that page to contact Mr Bryant Snr, and two others to send them messages claiming he had murdered him.
Dunfermline Sheriff Court heard McInroy had set up a Facebook page in a false name, Daniel Bunton, and used that to add Becky Gallacher - a friend of the missing man - to his friends list.
She then received a string of messages from that account - including claims he had taken Mr Bryant hostage and that his "life was at stake".
The next day Mr Bryant Snr received a message from an unknown person showing a message that had been posted on the "Find Allan Bryant Jr" page.
The message, from Daniel Bunton, read: "I am the killer of Allan Bryant.
"When he walked home I stopped my van, grabbed him, holded (sic) him hostage til I found out he was on the news so I brutally tortured him.
"Tied to a chair, stabbed nails in him, wrapped with 240,000 volt wire and fried that f****r Allah Akbar f*** white people."
McInroy shared the message on his own Facebook page, adding: "Sorry but the family need to know." He then had a conversation with himself between his own and the Daniel Bunton profile.
Mr Bryant Snr reported the incident to police. The next day McInroy contacted police saying he wanted to report threats made to him on Facebook by the Daniel Bunton profile.
Officers discovered the Bunton posts had come from a mobile owned by McInroy. In a police interview he confirmed he had claimed to have been the killer of Mr Bryant.
McInroy, 23, a prisoner at HMP Edinburgh, pleaded guilty to three charges of behaving in a threatening or abusive manner likely to cause fear or alarm.
McInroy admitted another charge over Facebook threats. He admitted threatening to put pictures of a three-year-old girl on pornographic websites last September 22.
For that he was given an 18-month community payback order with supervision and banned from using the internet.