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Trump has repeatedly said there was no collusion, and Russian Federation has denied interference.
The FBI also was able to obtain more than 700 pages of Cohen's encrypted messages and call logs.
Prosecutors did not disclose the contents of the shredded documents or what was in the encrypted texts sent using the WhatsApp and Signal.encryption apps.
US District Judge S. James Otero said Michael Cohen had failed to provide evidence that he would suffer "irreparable injury" without an immediate restraining order against Michael Avenatti.
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".
Cohen's attorney, Stephen Ryan, did not immediately respond to a request for comment.
The switch in legal team comes as Cohen's lawyers have until today to finish reviewing 3.7 million files seized in the Federal Bureau of Investigation raid for attorney-client privilege.
Daniels, whose real name is Stephanie Clifford, is suing Cohen and Trump to get out of an agreement under which Cohen paid her $130,000 U.S. not to discuss an alleged sexual encounter she had with Trump. She has alleged a sexual encounter with Trump in 2006.
Asked by reporters Friday if he was anxious about Cohen cooperating, Trump said, "I did nothing wrong, nothing wrong".
This new development arrives amid a period of uncertainty in Cohen's legal defense.
"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.
Agents seized paper files, computerized documents and phones from Cohen's home, safety deposit box and office in April.
Barbara Jones, the retired judge named to help in the document review process, recommended that the judge overseeing the case extend the deadline to June 25.
A source familiar with the matter tells ABC News that among the reasons for Cohen's change in counsel is a fee dispute. But the Federal Bureau of Investigation has not yet been able to extract anything from the second device.
Jones reported last week that of the first 300,000 items reviewed, she had determined that just 162 of them were covered by attorney-client privilege.