The federal government challenge to the Administrative Appeals Tribunal finding could test freedom of speech for public and private sector employees as lawyers spar over former public servant Michaela Banerji's right to post criticisms of asylum seeker policy while working for the department.

Lawyers for Ms Banerji, who was dismissed over the tweets in 2013, are not expected to oppose the move sending the case to the High Court and will look for a senior legal counsel to represent her when it hears the government's arguments against the appeals tribunal decision.

The Australian Human Rights Commission also intends to enter the case and make submissions about human rights issues it raises including the right to freedom of expression and the right to participate in public affairs, but will not represent Ms Banerji.

A government spokesman said Mr Porter would remove the government's Federal Court appeal against the finding and send it to the High Court. The move flags the case's potential implications for the government's policy on its employees' social media use.

"This decision reflected the importance of the case in terms of the administration of the Public Service Act across the public sector," a government spokesman said.

Lawyers for Ms Banerji want the federal government to pay her court costs regardless of the outcome, which they said would let them find a senior counsel experienced in High Court cases and equipped to argue her cause against the government's legal team.

Canberra-based lawyer Allan Anforth, representing the former Immigration official, said it would be a test case with consequences for federal and state government public servants and workers employed under private sector enterprise agreements and the federal workplace award.

The appeals tribunal's decision in April redirected scrutiny to the department's dismissal of Ms Banerji for tweeting criticisms of detention policies, and challenged new Australian Public Service rules stopping public servants from expressing their political views on social media.

It blasted the government decision to sack her, saying it "impermissibly trespassed upon her implied freedom of political communication", and "with a law only weakly and imperfectly serving a legitimate public interest".

Ms Banerji took the government to the tribunal after federal workplace insurer Comcare refused to compensate her for the psychological condition that developed after she was sacked over tweets from a pseudonymous Twitter handle @LaLegale.

The tribunal overturned Comcare's decision and found she suffered depression and anxiety that could be classed an injury under federal compensation laws.

Ms Banerji was working in the Immigration Department when co-workers learnt she was behind tweets railing against the government's treatment of asylum seekers.

She lost a high-profile attempt to stop her dismissal in the Federal Circuit Court in 2013, a decision seen as likely to curtail other bureaucrats' use of social media when judge Warwick Neville found Australians had no "unfettered implied right (or freedom) of political expression".

Her tweets did not disclose confidential departmental information, but an internal Immigration Department investigation in 2012 found she had breached the code of conduct for government employees.

In a submission to the appeals tribunal, Mr Anforth previously said the tweets had been posted from her own phone and, in most cases, outside work hours.

The appeals tribunal found the Immigration Department itself had identified Ms Banerji after she posted anonymously, and said guidelines stopping public servants from publicly criticising the government should not be applied to anonymous comments.