The Long War Journal, a project of the Foundation for Defence of Democracies, has based its report on the 20th edition of Al-Masra magazine -- affiliated with the Al-Qaeda in the Arabian Peninsula -- published in late August, which said the prisoners' swap took place weeks ago.
However, the news could not be independently verified as there has been no reports on the abduction of Kayani's son, who was not named in the report.
"If the jihadist organisation is merely boasting, then that is noteworthy. But if al Qaeda did manage to kidnap Kayani's son and force the Pakistani government's hand, then this indicates Zawahiri's men have a disturbingly long reach inside of Pakistan," the report said.
"Although retired, Kayani is one of the most powerful figures in the Pakistani military and intelligence establishment, which has long sponsored jihadis, including the al Qaeda-allied Taliban," the report alleged.
It said the editors of the Al-Masra magazine included a box highlighting the story on the frontpage saying "detaining" the "son of the Pakistani army commander" led to the release.
The newsletter's authors claimed a series of tweets posted online in mid-August provided the insider details of the story.
In a tweet, a jihadist accused the Pakistan Army of detaining Zawahiri's daughters, as well as the daughter of Sheikh Murjan Salem al Jawhari, as part of its "infidel" war on the mujahideen.
The twitter account has now been suspended.
"The twitter user, who is likely an Al-Qaeda media operative, further claimed that Al-Qaeda was left with two ways to deal with the situation. First, Al-Qaeda needed to take 'revenge' on the supposed spy. Second, Allah 'enabled the mujahideen' to detain the son of the Pakistan Army commander in order to exchange him 'for the sisters'.
"He included a picture of Kayani to emphasize that this is the Pakistani leader he meant. Al-Qaeda's account referred to Kayani as if he is active, even though he has been retired for nearly three years," the report said.
According to the media account, the army initially "refused" the proposed exchange, but eventually agreed after lengthy negotiations.
Zawahiri's daughters and the other woman, along with their children, were reportedly returned to Egypt.
"It isn't clear if the purported exchange took place in late July or early August," the report said.
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