He said he would would "get the b*tch" and "put two bullets in the back of her head", the court heard.
In the course of the investigation, police discovered Coulson's phone contained a document dealing with bomb-making, projectile weapons, handguns, ammunition, rockets and cannons.
He also had "a wide range of extreme right wing material and propaganda including racist and antisemitic imagery," police said.
But he was not charged for the threats against Ms Berger because the only witness was a fellow bail hostel resident and there was concern about how likely a conviction was.
Coulson, from Mexborough, South Yorkshire, had a previous conviction in 2017 for making a pipe bomb in his Nazi memorabilia filed bedroom. He was not named at the time as he was under 18. He received a youth rehabilitation order.
During that trial, the court heard he had been a member of the neo-Nazi National Action group, which is now proscribed as a terror group, and praised the 2016 murder of MP Jo Cox by a far right extremist.
The JC understands Ms Berger was told about the arrest of Coulson but was not made aware of his upcoming trial.
In court, Coulson admitted possessing The Big Book Of Mischief, which contained information useful for someone wanting to commit a terrorist act.
Detective Superintendent Simon Atkinson, from counter terrorism policing north east, said: “Jack Coulson was in possession of disturbing and potentially dangerous material, which indicated an extreme right wing mind set and an interest in home-made explosives.
“He hadn’t come across this material by chance, but had actively searched for it and downloaded it. While no evidence was found to suggest Coulson was planning to act on this information, the combination of this material and his ideology is very concerning.
“This case also highlights the dangers of material that is readily available on the Internet, material that could be misused, or used for a terrorist purpose. Searching for and storing information of this nature has the potential to put the safety of others at risk will not go unprosecuted. In the wrong hands it could have serious consequences.”
In February 2017, John Nimmo, 28,was jailed after making antisemitic death threats to Ms Berger and telling her she would "get it like Jo Cox."
She had received a number of emails from Mr Nimmo that included an image of a kitchen knife, as well as warnings telling her: “You better watch your back Jewish scum.”
