The full court of the Federal Court on Wednesday found Mr Brandis was obliged to help correct a miscarriage of justice as a fundamental aspect of the criminal justice system.

Mr Brandis could be now ordered to refer the case to the Court of Appeal of Western Australia so it can consider quashing the conviction.

Ali Yasmin, who came to Australia as a crew member aboard an asylum seeker vessel in 2009, was 14 when he was locked up in an adult prison, despite the authorities possessing proof of his youth.

Yasmin spent almost two years behind bars before he was granted early release and returned home to the island of Flores in 2012.

Yasmin has petitioned the Commonwealth Attorney-General to have his case referred to the WA courts so his conviction can be quashed on the grounds he was a minor at the time, in accordance with a government policy not to prosecute children.

That would then open the way for him to sue the government for wrongful imprisonment.

Mr Brandis has so far resisted making the referral, and court action to force a decision failed earlier this year.

In February, Justice Jayne Jagot found the Commonwealth Attorney-General had no legal duty to consider Yasmin's request and dismissed the case with costs.

Yasmin's lawyers appealed that decision, arguing Justice Jagot erred in her interpretation of the law.

The full court – Justice Susan Kenny, Justice Alan Robertson and Justice Debra Mortimer – on Wednesday allowed the appeal, finding the Attorney-General was obliged to consider and determine the matter.

The judges said the requirement to correct a miscarriage of justice was a fundamental aspect of any system of criminal justice.

"It is integral to public confidence in the criminal justice system, and to ensuring the system operates fairly and within the law, while acknowledging that any system operates imperfectly and what is important is that there is always a capacity for correction," the judges wrote.

"If there is no duty to consider whether to exercise the power, as the [Commonwealth] submits, then a petition can lie unattended and unexamined, or a deliberate decision can be made not to consider to exercise the power."

The judges sent the matter to Justice Jagot to be redetermined, and ordered the Commonwealth pay Yasmin's legal costs of the appeal.

Yasmin's lawyer, Sam Tierney, from Canberra firm Ken Cush & Associates, said his client was pleased with the decision.

"Mr Yasmin thanks the court for considering his matter," Mr Tierney said.

"He is pleased that he now has an opportunity to continue the fight to clear his name."