In a majority verdict on Wednesday, the court found that an original decision to convict Zainab Abdirahman-Khalif should stand.
It held that the trial judge neither conflated the physical and mental elements of the offence nor failed to give the jury sufficient guidance on what constituted steps to become a member of a terrorist organisation.
“The trial judge’s summing up though imperfect, was not unbalanced,” the court said.
It found that it was open to the jury to be satisfied beyond reasonable doubt that the accused took steps to become a member of terror group Islamic State.
It said the provisions creating the offence must be taken to extend to groups devoid of structural hierarchy that function in secrecy, with little formality, without a written constitution or set of rules, and without a contractual relationship between members.
Abdirahman-Khalif was rearrested after the judgment was handed down, although her lawyers are expected to ask that she not serve any more time behind bars and be released on parole.
In 2018, the 25-year-old was found guilty in the SA Supreme Court of being a member of IS and was jailed for three years.
Prosecutors had alleged she had communicated with other members of the group and organised a trip to join IS before she was arrested.
The former student was first stopped by police at Adelaide Airport while trying to board a plane to Istanbul, Turkey, in July 2016.
She told officers she was taking a last-minute holiday, despite having a small amount of clothing, no return flight and less than $200 in funds.
The Somalian refugee was later released but arrested at the Port Adelaide TAFE SA campus in May 2017, following a police investigation.
In sentencing, Justice David Peek said Abdirahman-Khalif had repeatedly expressed support for IS and jihad by playing chants about martyrdom, infidels, extreme violence, killing and death.
But in a decision last year, the Court of Criminal Appeal quashed her conviction and set her free, ruling it was not supported on the evidence.
In July this year, Abdirahman-Khalif was also hit with a wide-ranging control order by the Federal Court limiting her movements and her access to the internet.
In response to an application from the Australian Federal Police, the court imposed 19 individual measures to assist in preventing a terrorist act or the provision of support for a terrorist act.
Under the controls imposed, Abdirahman-Khalif is subject to a curfew from midnight to 6am each day, is barred from leaving Australia, and is barred from accessing or possessing any materials related to suicide or terror attacks and bombings.
She is only allowed access to one mobile phone, which must be presented to the AFP for inspection, and has been barred from accessing a range of websites and web applications.
They include messaging services such as WhatsApp and social media sites such as Instagram, Snapchat and Twitter.
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