The prosecutors said in their filing in Manhattan federal court that they had turned the materials over to Cohen's lawyers.
Friday's filing indicates that the government and Cohen's lawyers have agreed to a June 25 deadline for Cohen's team to examine the new material, which also includes new data recovered from a Blackberry that the Federal Bureau of Investigation had only recently been able to access.
At the time, prosecutors had not yet provided Cohen's lawyers with the reconstructed shredded documents or the encrypted messages.
Wood has ordered the feds to turn over all the seized material to Cohen and Trump so that they can flag documents they think are protected by attorney-client privilege.
Prosecutors agreed to extend that deadline by 10 days, if the judge approves. Trump has denied her allegations.
Cohen's attorney, Stephen Ryan, did not immediately respond to a request for comment.
Yemen: Saudi-led coalition begins battle for vital port
The Houthi-run Al Masirah satellite news channel claimed rebel forces hit a Saudi coalition ship near Hodeida with two missiles. Aid groups have pulled staff from the town over the deteriorating security situation and warned of catastrophic consequences.
"Mr. Avenatti either needs to respect and observe the Code of Professional Conduct (for lawyers) or remove himself from this case", Cohen's lawyer Brent Blakely said in an email.
Michael Avenatti, who represents Daniels in separate civil litigation against Cohen and Trump, on Friday tweeted that the encrypted messages and reconstructed documents "could pose a huge problem for Mr. Cohen and ultimately Mr. Trump".
The friend, who spoke on condition of anonymity, also told Reuters that Cohen has complained that he does not feel he has received enough support from Trump in dealing with the situation.
Cohen filed for a restraining order late Thursday against Avenatti to prevent him from speaking to the press about the adult film star's lawsuit against Trump and Cohen, which aims to nullify a 2016 hush agreement over an alleged affair between her and Trump.
Judge James Otero of the US District Court for the Central District of California set a briefing for later this month, after which he'll make a final decision on the restraining order request.
According to a report in arstechnica.com on Saturday, a letter submitted to the presiding judge in the case against Cohen revealed that the Federal Bureau of Investigation recovered over 700 pages of messages and call logs from encrypted messaging apps on a smartphone belonging to Cohen.