Alice Leek, who now identifies as a male and is named Sam Leek, was serving time at HMP New Hall in Flockton when he sent the letter to a male he is prohibited from contacting by a restraining order.
Leeds Crown Court was told that Leek and the male had been a relationship for around four weeks in 2016 and had met through a football team for people with learning difficulties.
Prosecutor Charlotte Noddings said the letter from 28-year-old Leek was intercepted by the male's mother.
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It read: "You deserve to rot in hell for what you have done. I will come and kill all of your family."
The court was told it was the third malicious letter Leek had sent to the male, who has learning difficulties and the mental age of a teenager.
Leek, who has 23 convictions for 43 offences, admitted a charge of sending a threatening letter and breach of a restraining order.
Mitigating, Bianca Brasoveanu said: "The defendant realises how serious this case is. He does not seek to minimise the seriousness of his actions.
"He never anticipated the letter reaching the address in light of the fact the prison was aware of the prohibition to send letters to that address."
She said that Leek apologised to the family for the distress and added: "There was no intention to carry out the threat in the correspondence."
The judge, Recorder David Gordon, gave Leek a 12-month jail sentence, but suspended it for two years.
He also said that Leek must wear a GPS tracker with an exclusion zone to keep him away from the male and his family. This will last for two years.
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