Arico was jailed in 2017 for offences including extortion but he claims his right to a fair trial was subverted and a miscarriage of justice took place because his lawyer was a police informant.
Gangland lawyer Joseph Acquaro was never officially registered as an informant although it was later revealed he shared information to police about another one of his clients, crime boss Frank Madafferi.
Mr Acquaro was shot dead outside his East Brunswick gelato shop in March 2016.
Arico's barrister Jason Gullaci SC last month told the Victorian Court of Appeal that Arico trusted Mr Acquaro and relied on him for legal advice across a 10-year period.
Mr Gullaci said Mr Acquaro re-engaged with police in April 2014 after a man, who can't be named for legal reasons, facilitated a meeting between the lawyer and police.
Mr Acquaro stayed in contact with the man for about a year, including at the time Arico was arrested in March 2015.
The man has already disclosed to the court 69 text messages and a log of 356 phone calls.
While there were no explicit references to Arico, Mr Gullaci said the messages showed the man asking Mr Acquaro about his meeting with police.
Mr Gullaci sought a court order for the unnamed man to provide more text messages and other conversation material.
Judicial Registrar Deirdre McCann has made that order, finding it was in the interest of justice that further material be disclosed.
"I have determined that there is legitimate forensic purpose in the documents sought," she said in her written judgment.
The unnamed man must produce all material that records the correspondence he had with Mr Acquaro about Arico between January 1, 2014, and March 15, 2016.
He has also been ordered to disclose communication he had with Victoria Police about Arico between January 1, 2014, and February 28, 2017.
The material the man must provide includes emails, text messages and file notes.
"Although there may be some uncertainty as to whether it is on the cards that the applicant will find material assistance in the documents disclosed, it is in the interests of justice that production be ordered," Judicial Registrar McCann said.
Arico was in 2017 jailed for 14 years, with a minimum of 10 years, for extortion, intentionally causing injury, possessing a firearm and drug trafficking.
His jail term was later cut by two years, with a minimum period of nine years, following an appeal.
10°C