Previously, he led AT&T's work before the Federal Communications Commission as the company's senior vice president for regulatory affairs.
The payment was the first known activity involving Essentials Consulting, a shell company incorporated in DE by Cohen.
The e-mail comes after revelations that AT&T agreed to pay $600,000 to Cohen a year ago in exchange for advice on how to approach the Trump administration.
Avenatti has been in the spotlight over hush money claims that Trump's attorney Michael Cohen paid out Daniels.
Even though the pledge didn't apply, Brendan Fischer of the nonprofit Campaign Legal Centre said Cohen's arrangement shows that Trump has failed to "drain the swamp" in Washington as he promised he would do.
While his exact intent was not clear, Trump was likely reacting to reports that his lawyer Michael Cohen was paid hundreds of thousands of dollars by AT&T for a consulting gig that actually amounted to Cohen peddling his access to Trump.
The former New York City mayor previously said in an interview on Fox News that Trump reimbursed Cohen for a hush payment to porn star Stormy Daniels, when Trump's public position had been that he never knew about the payment at all. "What did the President believe he was giving to the companies in exchange for the payments?" Cohen did not respond to requests for comment.
The documents specified that Cohen, who was not a registered lobbyist, was to spend none of his time engaged in lobbying.
Companies often hire consultants to explain the federal bureaucracy to them.
Israeli soliders open fire on Gaza protesters seventh week in a row
The Israeli military said on Friday its troops were defending the border and "firing in accordance with the rules of engagement". The Hamas-run Gaza Health Ministry said that one person was killed and another 146 injured, The Times of Israel reported.
In other words: If AT&T hired Cohen to win the government's approval, AT&T wasted its $600,000. However, he noted that hiring the president's lawyer could trigger ethical questions.
Giuliani told The Associated Press on Friday that Trump was "surprised" to learn that Cohen, his longtime attorney and self-described fixer, brokered deals with companies looking to gain his knowledge about the president. "They didn't get the result they wanted".
In fact, AT&T says it's done exactly that with previous administrations too. Months earlier, Trump had come out strongly against the proposed merger with Time Warner, which owns CNN - a network he often berates as "fake news".
Rudy Giuliani, President Donald Trump's lead defense attorney, on Saturday walked back his earlier admission to HuffPost that Trump intervened in the Time Warner-AT&T merger to try to kill the deal. He called the hiring of Cohen a "big mistake". "They didn't get the effect they wished".
Trump frequently railed against the AT&T merger on the campaign trail, calling it bad for the country. "We have received no additional questions from the Special Counsel's office and have considered the matter closed", it said.
Giuliani's particular reference to the president denying the merger is in distinction to feedback from final November when the Division of Justice's Assistant Legal professional Normal for the Antitrust Division Makan Delrahim advised ABC Information, "I've by no means been instructed by the White Home on this or some other transaction below evaluation by the antitrust division".
Quinn started with the Bell system as an operator for Illinois Bell in 1980, before AT&T was broken up by the Justice Department in a landmark antitrust action four years later.
Some within Washington's cozy lobbying circles expressed bemusement that AT&T was apologizing for behavior that has become commonplace for corporations in the capital - paying for advice about the government's most powerful decision-makers. "Yesterday was not a good day for Novartis", Mr. Narasimhan wrote.