Flynn, a retired army general, was forced to resign as national security adviser in February 2017 after he was found to have misled Vice President Mike Pence about discussions he had with Russia's then-ambassador, Sergei Kislyak.
Mueller wrote Tuesday that numerous investigations "in which [Flynn] has provided assistance are ongoing". The retired three-star Army general, who spent 24 days as the Trump White House national security adviser, pleaded guilty on December 1, 2017, to lying to the FBI in the Trump-Russia investigation.
Trump has repeatedly lamented how Flynn's life has been destroyed by the special counsel's probe.
"Additionally, the defendant's decision to plead guilty and cooperate likely affected the decisions of related firsthand witnesses to be forthcoming with the (special counsel's office) and cooperate", prosecutors wrote, making clear they used Flynn as their entry point into understanding the campaign and transition.
Another highly anticipated filing is expected Friday from Mueller's office, detailing the lies that prosecutors say Manafort told them after his guilty plea.
Flynn began cooperating with the Russian Federation probe "shortly after" Mueller's team approached him, prosecutors said - and that early cooperation boosted investigators' understanding of what happened during the campaign.
According to Mueller's filing, Flynn has been helping investigators longer and on more Justice Department probes than had been previously known.
He was a close adviser to Trump during the campaign - and famously led a "lock her up" Hillary Clinton chant at the Republican National Convention. The special counsel in the Russian Federation investigation is set to give the first public insight into how much valuable information President Donald Trump's former national security adviser has shared with prosecutors. This, the officials felt, might somehow expose Flynn to Russian blackmail. Investigators could ask Comey specifically how the agents who interviewed Flynn characterized his answers and behavior.
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Flynn was not the first defendant in Mueller's probe to have made false statements to federal investigators, though he may be the first to not have to serve a prison sentence.
Of the 13 pages Mueller penned and filed late Tuesday, nearly half was redacted.
He is so far the only member of Trump's administration to plead guilty to a crime uncovered during Mueller's wide-ranging investigation into Russian attempts to influence the 2016 US election and potential collusion by Trump aides.
Previously, Mueller's office has told judges that the defendants they cut deals with did not help them as extensively. It doesn't say that he failed to provide substantial assistance to the investigation, as Mueller said in the George Papadopoulos sentencing memorandum.
"Several senior members of the transition team publicly repeated false information conveyed to them by (Flynn) about communications between him and the Russian ambassador regarding the sanctions", the filing states. It is a spare document, seven pages, along with a largely-redacted six-page supplement laying out what Flynn has done for Mueller.
Third, because the addendum to the sentencing memo is mostly redacted, one is left reading tea leaves in the document's redactions. A highly redacted addendum to the memo said that Flynn had helped the government with several investigations, including the Russian Federation probe, and done 19 interviews with the special counsel's office or other Department of Justice offices.
Flynn also admitted to making false statements about unregistered foreign agent work he performed for the benefit of the Turkish government.
"The fact that he is saying 'senior government leaders should be held to the highest standards, ' I would be a little nervous if I were the people involved in the obstruction of justice investigation, starting, of course, with the president of the United States."More news: Central Intelligence Agency director convinces senators of Saudi crown prince's role in Khashoggi murder
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