El-Shater, according to the former Brotherhood members and security officials, is suspected of running an information gathering operation capable of eavesdropping on telephones and email.
He was the Brotherhood's first choice for presidential candidate in last year's election but was disqualified over a Mubarak-era conviction.
Following his disqualification, he publicly said last summer that he had access to recordings of telephone conversations between members of the election commission and the military council that ruled Egypt for nearly 17 months after Mubarak's ouster.
The conversations, he claimed, were to engineer throwing him out of the race. He did not say how he knew of the contacts or their contents.
Again in December, he suggested that he had access to information gathered clandestinely.
Addressing Islamists in a televised meeting, he said he has "detected from various sources" that there were meetings of people allegedly plotting to destabilize Morsi's rule.
He did not identify the alleged plotters nor say how he had learned of the meetings.
A spokesman for the Brotherhood's political arm, the Freedom and Justice Party, said at the time when asked for comment that it was to be expected from a group as big as the Brotherhood to have its own "resources." That was taken as virtual confirmation of a parallel intelligence gathering operation.
Morsi was also seen as suggesting that the Brotherhood was spying on critics when he spoke to supporters outside his presidential palace in November. He said he had firsthand knowledge of what transpired in a meeting of several of his critics.
"They think that they can hide away from me," he said.
The words of El-Shater and Morsi were taken as strong hints that the Brotherhood has its own intelligence gathering operation. But in a country fed on a steady diet of conspiracy theories, no hard evidence has come to light, only suspicion and talk.
A former Brotherhood member, Mohammed el-Gebbah, claimed the group had six "mini intelligence centers," including one housed in its headquarters in the Cairo district of Moqqatam.
He did not provide evidence to back his claim and another Brotherhood spokesman, Murad Ali, denied that the group has such capability.
In an off-the-cuff remark, Brotherhood stalwart Essam el-Aryan said last October that Morsi's presidential palace secretly records all "incoming and outgoing communications." The president's spokesman swiftly denied it.
But it only fed the notion of a Brotherhood parallel intelligence gathering operation with Morsi's support and cooperation.
Another concern that has arisen is whether the Brotherhood might be running its own militias outside of government security agencies.
That fear arose from a wave of mass protests that turned violent in December. Protesters for and against Morsi faced off over decrees, since rescinded, that gave the president near absolute powers.
In early December, the Brotherhood posted a "general alert" on its official Facebook page and the next day, groups of armed Brotherhood supporters attacked opposition protesters staging a sit-in outside Morsi's palace.
Thousands of Morsi supporters and opponents poured into the area and street fighting continued well into the night.
Video clips later posted on social networks showed Brotherhood supporters stripping and torturing protesters in makeshift "detention centers" set up just outside the palace gates, partly to extract confessions that they were on the opposition's payroll.
On-camera testimonies by victims to rights groups spoke of police and palace workers standing by and watching as they were being abused by Brotherhood supporters.
At least 10 people were killed and 700 injured in the clashes on Dec. 5.
The next morning, groups of Morsi supporters staged military-style drills in residential areas near the palace.