A Tamil family fighting deportation to Sri Lanka are expected to learn on Tuesday if their latest bid to return to Queensland has succeeded.

Priya and Nades Murugappan and their Australian-born daughters Kopika and Tharunicaa, aged five and three, had a win in the Federal Court early in 2020, but that was appealed by the federal government.

Justice Mark Moshinsky had ruled that Tharunicaa was denied procedural fairness in making a protection visa application, which would have allowed her to remain in Australia.

He ordered their costs of $206,934.33 be paid, after determining that Immigration Minister David Coleman had lifted a bar to consider a visa application.

Nades and Priya, with daughters Kopika and Tharunicaa. The family are in detention on Christmas Island.

The family, from Biloela in Queensland, were taken into detention in Melbourne in March 2018 and transferred to Christmas Island in August 2019 after an urgent injunction prevented their deportation to Sri Lanka mid-flight.

The federal government appealed Justice Moshinsky’s findings, while the family’s lawyers filed a cross appeal against a second ground that was dismissed in that case.

An appeal hearing was expected to run over two days in October 2020, but took significantly less time after Justice Geoffrey Flick, one of three hearing the case, became “cranky” at the government’s barrister for repeating himself.

Their decision is expected to be handed down on Tuesday morning.

-AAP