Beghal, an Algerian who sometimes calls himself Abou Hamza, after his idol, once boasted that he had set up a vast network of terrorist cells in Britain, Germany, France and Spain.
Although Beghal's web of terrorist cells was thought to have been dismantled after he was arrested in 2001 following allegations of a bomb plot, he recruited Kouachi in prison 10 years ago, suggesting he was trying to build a new network.
Beghal was released from a 10-year sentence in 2010, and investigators will want to establish whether he could have used his contacts in the UK to set up sleeper cells in Britain.
French-Algerian Kouachi was jailed in 2008 for arranging for jihadists to travel to Iraq. In prison he met Beghal, jailed for "belonging to a criminal association in relation to a terrorist undertaking".
After the two were released from prison they remained close, and were photographed by French surveillance officers playing football in April 2010 in Cantal, southern France, with two other convicted terrorists, jihadi recruiter Ahmed Laidouni and Farid Melouk, an Algerian member of the GIA terror group.
Beghal was described as "a constant presence" at Finsbury Park Mosque for two years in the late 1990s, when it was Hamza's base.
He is said to have been particularly close to Abu Qatada, the Jordanian "spiritual leader" of al-Qaeda's European operations in the 1990s, who was extradited back to Jordan in 2013.
Reda Hassaine, who was a paid MI5 informant inside Finsbury Park mosque in the late 1990s and early 2000s, said Beghal was a familiar figure there.
"He was closer to Abu Qatada than to Abu Hamza," said Hassaine. "He definitely had connections with them. I believe he lived outside London at the time but he was regularly seen at the mosque and at the coffee shops around Finsbury Park.
"There is no doubt that you can see the influence of their teachings in him. Their warped view of the world has filtered down through him to a new generation.
"What happened in Paris was the legacy of Abu Qatada and Abu Hamza.
"A completely new generation, who have never met these people in London, have learned their ideology indirectly and are now willing to die in jihad."
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Beghal, 50, is known to have been a member of Takfir-wal-Hijra, a puritanical extremist group financed by Osama bin Laden before Bin Laden distanced himself from it for being too extreme - it regarded non-extremist Muslims as "infidels" and legitimate targets. Beghal was once described in a British court case as being so extreme Bin Laden considered him "beyond the pale".
At the time of the 9/11 attacks in 2001, Beghal was suspected by European intelligence agencies of being the man chosen by al-Qaeda to open a terror front in Europe.
After he was arrested at Dubai airport in July 2001, Beghal told his interrogators he would travel around Britain in the late 1990s recruiting young Muslims for jihad.
Among the many extremists who congregated at Finsbury Park Mosque, he was regarded as one of the most dangerous.
"Members of this group would kill their own father if they caught him smoking or drinking," said one moderate Algerian.
- Telegraph Group Ltd
