As the internet portal "Crux" reported on Friday, Figueroa, who used to belong to the "Marian Community of Reconciliation" (MCR), expressed her criticism in an open letter.
In it, she accused the MCR of "carrying the DNA of the Sodalitium", as it uses the same methods.
According to Figueroa, the tactic consists of saving the institution and "prioritising damage limitation over the truth".
The MCR would also "manipulate with half-truths without telling the whole story".
She described the latest accusations against the two Vatican investigators, the well-known abuse investigator and Maltese Archbishop Charles Scicluna and the priest and employee of the Dicastery for the Doctrine of the Faith, Jodi Bertomeu, as "perverse".
Reaction to the statement
Figueroa is a theologian and was one of the first members of the MCR, of which she was superior for a time.
When she uncovered the first cases of abuse, she was silenced by the community, according to media reports.
It was not until 2010 that she was able to present a report on the allegations of abuse, which identified several victims and perpetrators. Her letter is a reaction to the statement published by the MCR at the beginning of October, in which the management distanced itself from the latest allegations.
All links to the "Sodalicio", the male branch, had been officially severed, the statement said.
The current management knew nothing about the cases of abuse.
Nevertheless, the MCR leadership apologised for the misconduct and pain of the victims who "suffered abuse of power, manipulation of conscience or other forms of abuse in the communities".
The allegations would be "duly investigated".
In this context, Figueroa wrote that spiritual abuse in the MCR is not a thing of the past, but still occurs.
It was "common knowledge" that some women had submitted further complaints to the current Archbishop of Lima, Cardinal-designate Carlos Castillo. She described the distancing of the MCR as "despicable".
The MCR is one of four organisations founded by the Peruvian layman Luis Fernando Figari. The Vatican had already expelled Figari from his community in August following allegations of sexual abuse.
Following the conclusion of interviews and investigations, the head of the church expelled ten members of the lay group at the end of September. Among them was a bishop. They were accused of abuse of power and other misconduct.