The Merauke District Court on Tuesday announced the decision by the Jayapura High Court to overturn their convictions and to order their immediate deportation to Australia.
However, prosecutors have refused to process the paperwork for their departure, instead sending them notification of intention to appeal to Indonesia's highest court, the Supreme Court in Jakarta.
"It is now official, the prosecutor has lodged the notification of the Supreme Court appeal," said lawyer Efrem Fangohoy.
"I have signed the notification letter today.
"This shouldn't delay their departure, but I don't know."
Prosecutors have 14 days to lodge the basis for their appeal, while defence lawyers can lodge a rebuttal at the same time.
There is no deadline for a decision from the Supreme Court. Appeals can often drag on for years.
Their lawyers insist the group can leave Indonesia before a judgment from the Supreme Court.
However, prosecutors are refusing to release their plane from evidence, and the Jayapura court's original ruling stipulated that the group must leave aboard their own plane.
The group is seeking a document from the Jayapura court to authorise their departure on a plane other than their own, and have also sought intervention from the Australian government.
In the meantime, they are staying at the airport with their luggage.
The five, from Cape York on Australia's northern tip, had planned after their successful appeal to make the one-hour journey back to Horn Island in the Torres Strait, where they had embarked on their ill-fated joy-ride.
Initially suspected of being foreign spies, they claimed they had only wanted to spend a long weekend in West Papua for a holiday, and mistakenly believed they could get visas on arrival.
They were given permission to land the plane but were arrested upon disembarking.
In January, the District Court jailed Scott-Bloxam for three years and each of his passengers for two years.
There are strict restrictions placed on visiting Indonesia's western-most province, troubled by a low-level separatist insurgency since the 1960s.