Rabbi Cohen, former deputy headteacher at the school, told the boys to close down the group after Mia's death and Mr Murphy said it would have been helpful if the group chat had been "preserved" to see "what, if anything, it contained about Mia".
Emails suggest bosses at JFS "only became aware of the group chat after Mia's sad death", Mr Murphy said.
An email was sent to the school on March 17 about the group chat, the hearing was told.
Lily Lewis, counsel for Mia's brother Douglas Stewart, said a Snapchat group was "quite widely known of".
She said Mr Stewart wishes to put questions to Rabbi Cohen about what he knew either before Mia's death or in the immediate aftermath.
Rabbi Cohen said in a statement he thought "he'd done a good thing" but the family "would certainly disagree", Sefton Kwasnik, counsel for Mia's father, said.
Susan Jones, counsel for JFS, said the school has "always co-operated" in terms of information disclosure.
She said there could be multiple social media groups, adding: "There's nothing that's come to my attention that JFS were aware of any group chat prior to March 17."
Gary Lesin-Davis, counsel for Rabbi Cohen, said: "All the evidence points to the fact that he or the school did not know of the presence of this social media group."
He added: "How can the school or its employees act on something when it was not known?"
Mr Lesin-Davis said there are a number of social media sites included in the material for the inquest, including a group where "images and videos of girls" were shared.
Last month, the Metropolitan Police apologised after confirming they have lost a sim card from Mia's main phone and a second mobile.
Mr Janin told the hearing he will "not accept the telephone was lost within the police department".
Mr Murphy said that although the phone could not be found the data from it has been analysed.
Mr Murphy decided the group chat set up by some male pupils while Mia was at JFS is in the inquest's scope.
Mr Murphy said the events involving Rabbi Cohen have the potential to be relevant in relation to preventing further deaths as it "would have been helpful if the content had been preserved to see if anything in the content is about Mia".
He said Rabbi Cohen will not be called as a witness of fact but will be called as a witness in relation to preventing further deaths.
The inquest is set to take place over two days on a date yet to be confirmed in the New Year.
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