Ahmiri Ahmedi Azizi, aged 24, of Mount Street, is accused of sharing a video the day after Emad Al Swealmeen died when his device exploded in a taxi outside the hospital last November.
The video, encouraging terrorist attacks against the West, was transmitted on his public Instagram account, Manchester Crown Court heard.
Later that month Azizi allegedly viewed a video about making a silencer for a gun.
Azizi, who came from Iran to Sheffield “in the back of a lorry”, is accused of seven counts of disseminating terrorist materialvia social media between June and November last year.
His fellow Kurdish co-defendant, Mohammed Hussini, 19, also from Iran, is charged with four counts of the same offence by sending videos via Telegram between August and November last year.
Denise Breen-Lawton, prosecuting, said it was the Crown’s case both were Islamic State (IS) supporters intending to encourage terrorism, or were reckless as to whether they might.
She said the two defendants were communicating together through the chat function on Telegram from last April.
Azizi went on to set up an Instagram account and within a month he posted a video glorifying martyrdom, said the prosecutor.
Alongside the video were posted emojis of a raised index finger and black flags which were clear IS symbols, according to the Crown.
Miss Breen-Lawton told the jury: “On November 14, 2021 you might recall that there was a terrorist bombing at Liverpool Women’s Hospital.
“It was a shocking and horrific event in British history, as with any such bombing. It was widely reported on news channels and is a matter of public record.
“What did Mr Azizi do in response to that? He posted a terrorist propaganda video made by Islamic State, encouraging attacks against the West and the ‘Kuffar’ instructing methods of attack with knives and rifles.”
She added: “At the very time when the people of this country were recoiling in horror from a bomb attack on a hospital, Azizi was sharing a public video encouraging others to commit violent attacks on the West.”
The prosecutor said Azizi’s case is he believes his phone was hacked by or on behalf of the Iranian government, while Hussini will say his transmitted material was to assist fellow Kurds who were applying for asylum in the UK by highlighting how they were treated by IS.
John Jones QC, defending, said Azizi was a shepherd in Iran before being trafficked to the UK, adding: “He arrived in Sheffield in the back of a lorry and went to work in a car wash and then a takeaway.”
Azizi has aspirations that Kurdistan becomes an independent nation and was a vocal opponent of the Iran government and IS, he said, with rivalry and hatred between IS and the Kurdish people “bitter and divisive”.
He added: “The material on the defendant’s phone is in complete opposition of everything that he believes in.”
John Harrison QC, representing Hussini, from south east London, said his client came to the UK in 2018 via motor vehicle from Turkey.
The defendant was ‘previously detained and tortured by Iranian authorities’. His father was executed as a member of the Peshmerga military force, he said.
Mr Harrison said: “He believes IS share the same ideals as the Iranian state. He regards both as terroristic organisations who commit atrocities against sections of the Kurdish community.”
Hussini sought asylum and has leave to stay in the UK until 2026.
Azizi also denies viewing or accessing terrorist information and failing to disclose his phone PIN number.