First up, some brief corrections - Order of Suleiman and Suhhar Sulayman. Not a big deal.
Anyway, tradition holds that the magic of the Solomonic sahirs came from King Solomon himself, who possessed great knowledge and power, taught to him by the Green Man, Al-Khidr, who, the Quran says, taught Moses as well…and also traveled with Alexander the Great after becoming immortal by drinking the Water of Life. After the death of Solomon, his arts passed down in many secret traditions - including evil, Infernal methods that are propagated, it is said, by the angels Harut and Marut as a test of human faith. The Arts of Solomon spread and changed. In Persia, it became the Zoroastrian magics of the priests, while in Arabia it was deeply influenced by Islam.
Some say that the caliph Ali ibn Abi Talib, son in law to Mohammed, was guided by Al-Khidr in the Arts of Solomon, or by three wise men. This belief is often called on to support the idea that magic is not in itself evil or sinful or worldly - only its uses. Certainly, at some point later in the Umayyad dynasty, three summoners swore loyalty to the caliphs. They were given the title ‘wazir’ - a word that at the time meant ‘magician serving the caliph.’ They were initially untrusted, but their power against other wizard made them valuable, as the spirits they summoned could resist the magic of others. Soon, there were thirty wazirs, not three - and then a hundred. They developed their abilities as they spread Islam with the Caliphate’s armies, learning to summon and control things besides jinn. Their magic enable the Caliphs to overcome enemy sorcerers, and the Caliphate spread widely. This is likely the source of the Order of Hermes’ original fears of the Order of Suleiman, which at the time didn’t really exist per se.
However, the Umayyad wazirs were callous towards the spirits they enslaved, even though many jinn and spirits were themselves Muslims. This tainted their ways, turning many supernatural beings against them, and the jinn declared war upon them. By 720 AD, they were unable to support the Caliphate due to the constant attacks by spirits on their homes. It is believed this is a major reason why the Umayyad advance slowed. This didn’t help things for the Umayyads politically, and they were overthrown by the Abbasids not long after. The Abbasids were more than happy to hand the wazirs over to the angry jinn, and the wazir tradition was largely wiped out as the Umayyads collapsed.
Jump forward to the 780s and the rise of Harun al-Rashid, wisest of the Abbasid Caliphs. His mother, Al-Khayzuran, was a mystic of Yemen, who knew the magic of song and story. She convinced her son to form a council of wizards to advise him on magic and to help secure the Caliphate - though Harun always preferred scholarly types to warriors. The head of the council was the grand vizier of the Caliphate - Yahya ibn Khalid, called the Barmakid, a scholar without the Gift who dabbled in alchemy and had been Harun’s tutor. Yahya invited the wisest scholars to join this so-called ‘Solomonic’ council.
Five scholars answered the call, forming the council alongside Yahya and Al-Khayzuran. First was Jabir ibn Hayyan, an alchemist and summoner with a gentle Gift, who was master of the art of Sihr - the remnant of the wazir tradition of the Umayyads, by which they called on many spirits. It was Jabir who allowed the council to combine their many arts into a single tradition.
Second was Muhammad al-Fazari, an astrologer and scholar who wrote many books. He is said to have invented the armillary sphere, and was guided by a spirit that had once been his father, Ibrahim, who taught al-Fazari how to initiate the un-Gifted into the mystical powers of the sahirs.
Third was the Nestorian from Persia known as Bakhtyshu. His father, Jurjis ibn Bakhtyshu, had served the last Caliph, but because the family was Christian, Bakhtyshu’s membership on the council was provisional and that only because Yahya insisted on his presence. However, he proved himself by exorcising a potent demon plaguing Harun al-Rashid, and he taught the First Council the true names of many spirits.
Al-Zill Habib, the Beloved Shadow, was a highwayman and popular rebel against the Umayyads who led an army of loyal followers that included some jinn and yatus (a form of Persian faerie wizard). It is believed that he was a relative of Al-Khayzuran, but even when alone he was always cloaked and hid his face.
Last was Al=Hajjaj, also known as Al-Majnun, the Madman. He was a poet and mathematician who saw visions and claimed to have studied under Al-Khidr himself, and to have drunk the Water of Life. Certainly he never aged visibly from the appearance of 25, and none ever knew his birthplace.
Between them, the seven developed a theory that allowed them to explain their arts to each other, combining their summoning abilities and forming the Solomonic Arts. The council answered directly to the caliph and were to teach each other magic. Each excelled at one part of the Arts of Solomon. Eventually, Al-Khayzuran died mysteriously - she retired one night in 789, complaining of a headache, and then vanished in full view of several courtiers. The council mourned her, and Yahya retired soon after, leaving his seat to his Gifted son, Ja’far, who became Harun’s grand vizier and, eventually, his sole point of contact for the wizards, whom Harun drew away from over time.
It is said that Harun grew mistrustful of Ja’far and the sahirs, seeking out other wise men to listen to, including, or so legend says, a Hermetic magus from the court of Charlemagne, who was named Christopher Coronus, and a Sufi mystic named Fozail-e Iyaz, as well as a strange miracle worker from the east named Dawud al-Kharita. Harun began to resent the sahirs, and rumors of Ja’far being an evil sorcerer spread. It is said that eventually Ja’far was executed after he convinced Harun’s sister to plead on his behalf. Others claim that Ja’far had grown too ambitious and powerful and attempted to force Harun to make him the heir to the Caliphate by marrying his sister, and rightly deserved his execution.
The remaining five councillors became quite scared, as they had now lost all contact with the court. They traveled to the prison where Yahya had been kept, his life having been spared, and decided with his advice to form their own independent organization, serving the Caliphate more indirectly that they might avoid court intrigues. This they named the Suhhar Sulayman, the Summoners of Solomon. They begged Harun to be allowed to form this, convincing him it was no plot against him and promising that the members would still be loyal subjects. Thus was the Suhhar Sulayman formed - and it remains in existence even to today. The descent from the wazirs of the Umayyads is why even now the wizards of the Suhhar name themselves ‘viziers’ and their leader the ‘grand vizier.’
The Iberian sahirs stopped attending the Suhhar by the 910s, and the rise of the Fatimids in Egypt drove many North African sahirs into Egypt, to avoid conflict with the potent Berber wizards. Now, the Suhhar’s control is broadly Egypt, Arabia and Persia. Their long peace was interrupted when Hasan i-Sabbah and his assassins murdered the grand vizier and fled to Persia, having stolen the secrets of sorcery. Now, the Nizari Isma’ili that serve him are foes of the Suhhar but wield the same abilities. The biggest problem they face, however, are the Crusades, and how to fight the Crusaders. They have, however, offered the hand of peace to the Order of Hermes - the better to watch the Hermetics and learn what they can do, and the better to be prepared if the Suhhar decides they must attack. They view Hermetics as an enemy that must be studied, to help win the war against the i-Franj attacking their lands - even if they don’t plan to fight the Hermetics directly.
The sahirs are operating independently of the two main Arabic generals, Nur ad-Din and Salah ad-Din. Nur refused their aid because he didn’t want to join the Suhhar and had been taught magic by Al-Khidr himself, while Salah ad-Din gave no reason for his refusal.