Lawyers for Cardinal George Pell have lodged a special leave application with the high court to try to appeal his historical sex abuse convictions, which will be his final avenue to have his conviction overturned.

The high court on Tuesday confirmed it had received the application through its Melbourne registry.

The lodging of the appeal does not mean the high court will agree to hear the case. First, the matter will be considered by a panel of two to three judges, and will either be dismissed or approved. The parties may be called to a brief hearing for further consideration. A decision about whether special leave to appeal will be granted is usually made on the same day as the hearing.

At least five and sometimes all seven justices of the high court will hear the appeal if it is granted. The appeals process can take several months, and is unlikely to be considered before 2020. In the meantime, Pell remains in Melbourne assessment prison, receiving letters and visits from his supporters. Pell has maintained his innocence throughout the process.

The 78-year-old was sentenced to a six-year prison sentence for sexually abusing two 13-year-old former choirboys at St Patrick’s cathedral when he was the archbishop of Melbourne in 1996. He will be eligible for parole after serving a term of three years and eight months.

In August, the Victorian court of appeal – the highest court in the state – dismissed Pell’s appeal. He had 28 days to appeal to the high court, with lawyers filing his application at the 11th hour on Tuesday. However, filing at the last minute is not unusual.

The jury had not been unreasonable in convicting Pell on one count of sexual penetration of a child under the age of 16 and four counts of an indecent act against a child under the age of 16, the Victorian court of appeal chief justice, Anne Ferguson, and appeal court president justice, Chris Maxwell, previously found.

A third judge, Mark Weinberg, disagreed, finding the complainant was inclined to embellish aspects of his testimony and that he could not exclude the possibility that some of what he said was concocted. But in the court of appeal, judges are required only to reach a majority decision, which meant Pell’s appeal failed.

But in the appeal filed to the high court, Pell’s lawyers say Ferguson and Maxwell were wrong. “There did remain a reasonable doubt as to the existence of any opportunity for the offending to have occurred,” the filing said.

“The majority [of judges] erred by finding that their belief in the complainant required the applicant (Pell) to establish that the offending was impossible in order to raise and leave a doubt.”

In a criminal trial it is up to prosecutors to establish proof, not the defendant to prove innocence, and the filing says the Victorian appellant judges wrongfully reversed this onus of proof.

One of Pell’s victims died of an accidental drug overdose in 2014 at age 30. His father is being represented by Lisa Flynn from Shine Lawyers. She said her client was “beyond disappointed” to hear of the appeal.

“This painful period of his life is simply not coming to an end which continues to take a toll on his health,” Flynn said. “Every time Pell takes his legal fight to the next level our client is reminded of the disgusting abuse he inflicted on his son as a young choirboy.

“He has no doubt George Pell sexually abused his son and that his son’s sudden turmoil and devastation of his life was a direct result of the abuse he suffered inside Melbourne’s St Patrick’s cathedral at the hands of George Pell. Although he knew this was a possibility, it is still very hard for him to take when his son’s abuser was found guilty by a unanimous jury.”