Muhammad Yusuf, a charismatic Muslim preacher, founded the group in 2001 from his base in the Railway suburb of the Borno state capital, Maiduguri.
His followers at the time were disgruntled young people, who met at Yusuf's "Markaz" (centre in Arabic), which comprised a mosque and his living quarters.
Yusuf conducted fiery sermons from the mosque calling for jihad (holy war) against what he perceived to be a corrupt, secular government.
"The Boko Haram insurgency is a turning point in the history of Borno state and the northeast. Our history cannot be written without reference to Boko Haram," he told AFP.
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"We want to document it for posterity to have a clear and correct picture of what happened."
The rebuilt "Markaz" would house "all objects related to the insurgency", he added, rejecting the possibility that it would immortalise Yusuf.
The building has been in ruins since it was reduced to a pile of rubble in the July 2009 military crackdown against the group that is taken as the start of the insurgency.
Some 800 people were killed, most of them members of the groups.
Since Yusuf's deputy, Abubakar Shekau, took over, Boko Haram has developed into one of the world's deadliest jihadist groups.
At least 20,000 people have been killed and more than 2.6 million others made homeless in its quest to establish a hardline Islamic state in northeast Nigeria.
It achieved global notoriety when fighters kidnapped more than 200 schoolgirls from the town of Chibok in April 2014.
A fort built by Rabe, a tyrannical Sudanese raider who conquered the former Kanem-Borno empire in 1893, was turned into a national monument, he added.
It is situated in the town of Dikwa, some 90 kilometres (nearly 60 miles) from Maiduguri. "Rabe was just like Muhammad Yusuf," said Bulama.
Last December, Borno state governor Kashim Shettima, announced plans to convert Boko Haram's "Camp Zairo" enclave in the Sambisa Forest into a museum.
There have since been indications that Boko Haram fighters have returned to the camp, despite denials from the military.
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