Brendan McConville claims the Prison Service failed to ensure he can safely use computer facilities to complete an Open University course in criminology and psychology.
The 48-year-old was granted leave to seek a judicial review after a judge ruled he has established an arguable case.
Lord Justice McCloskey indicated a full hearing should now take place before the end of the year.
McConville, from Craigavon, Co Armagh, is serving at least 25 years behind bars for the murder of Constable Carroll 10 years ago.
A second man, 28-year-old John Paul Wootton, from Lurgan, Co Armagh, was handed a minimum 18-year term for his part in the assassination.
Constable Carroll, 48, was the first police officer to be killed in Northern Ireland after the formation of the PSNI.
He was ambushed and shot dead by dissident republicans as he responded to a 999 call at Lismore Manor, Craigavon in March 2009.
A circumstantial case involving DNA evidence helped to secure the murder convictions, including gun residue on a coat linked to McConville recovered from a car said to have been used by the killers.
He is among 40 republican and loyalist inmates held within a separated regime at the high security HMP Maghaberry.
The court heard he is in the final stages of a Bachelor of Science honours degree in criminology and psychology studies.
Proceedings were brought against the Prison Service for an alleged failure to provide access to the necessary internet resources.
Counsel for McConville said his client was in segregation at Maghaberry for safety reasons.
He argued that it was irrational for the authorities to say the convicted killer can use the facilities by simply leaving the separate regime.
According to McConville’s legal team it amounted to a difference in treatment.
Lawyers representing the Prison Service rejected assertions that he was never offered use of the education suite, stressing it is located in a special unit open to all within the jail.
The challenge had been deferred to allow time to consider a report into learning opportunities for separated inmates and a potential complaint to the Prisoner Ombudsman.
But in court today Lord Justice McCloskey confirmed he was granting leave to apply for judicial review.
Following the ruling McConville’s solicitor, Gavin Booth of Phoenix Law, said: “My client is challenging the refusal to allow him access to the computer suite for the purposes of degree work, which requires online material.
“Hopefully this will give all prisoners the same rights, entitlements an access to education provisions.”