Australian Border Force boss Roman Quaedvlieg has collected about $500,000 in wages while on paid leave, while allegations he had a relationship with a junior staffer are investigated, Senate estimates has heard.

A nine-month investigation into the conduct of Mr Quaedvlieg is now being overseen by the head of the Department of Prime Minister and Cabinet, a Senate committee was told on Monday.

Mr Quaedvlieg, who reportedly earns about $618,000 a year, is on full pay during the investigation.

Home Affairs secretary Michael Pezzullo, who appeared before the Senate Legal and Constitutional Committee, said he could understand Mr Quaedvlieg’s frustration that the investigation had taken so long.

“I can certainly understand why he is frustrated. It is frustrating to a lot of people. But there’s also people who have to discharge their duties with professionalism and conscientiously,” Mr Pezzullo said.

Mr Quaedvlieg has been on leave since late May amid an investigation into allegations he helped a junior staffer, with whom he had a relationship, secure work at Sydney airport.

He reportedly denies he helped the woman get the job – and there are reports that the allegation, if proven, is not serious.

Mr Pezzullo received a report into the investigation late last year but was tight-lipped on its status.

Crossbench senator Derryn Hinch said it did not make sense a report was produced three months ago but Mr Quaedvlieg was still off duty.

“It might well be the case that it doesn’t make sense, senator, but the processes are being applied very diligently,” Mr Pezzullo replied.

In a curious twist, another investigation into how Mr Quaedvlieg’s official Twitter account happened to ‘like’ a pornographic video while the Border Force chief was on leave has not uncovered the culprit.

Six departmental staffers had access to the account.

Immigrations officials asked the Australian Commission for Law Enforcement Integrity (ACLEI) to look into the case and have been handed a final report.

“They found no evidence that Mr Quaedvlieg used the official ABF commissioner’s account to ‘like’ a tweet containing a pornographic clip from an account under the name Lady Mystique,” Home Affairs deputy secretary Rachel Noble told the committee.

Che Quadvlieg was fined $500 after being caught with a small bag of the street drug ecstasy. Photo: AAP

“ACLEI also found no evidence of who had ‘liked’ the tweet, or whether the ‘like’ was accidental or intentional.”

Ms Noble could not rule out the possibility his account was hacked.

“I think what ACLEI have told us is that they have no evidence one way or the other,” she said.

In another blow to the Quaedvlieg family, the Border Force boss’ son, Che Roman-Dujon Quaedvlieg, pleaded guilty in January in a Brisbane court to one charge of drug possession.

Meanwhile, estimates also heard that Mr Pezzullo’s annual salary increased from $745,000 to $788,000 (including superannuation) after moving from his role as chief of the Department of Immigration and Border Protection to head up the new Home Affairs super portfolio.

-With AAP