The introverted, anarchical punk-goth hacker heroine of the Girl With the Dragon Tattoo novels had always intrigued Karin Smirnoff. In fact, the eponymous Lisbeth Salander was the reason Smirnoff read all six books in the series. So when the Swedish writer was approached to continue Salander’s story and write a seventh novel, her answer was an automatic “Yes”.

Smirnoff is the first woman to write for the Millennium series, which began with a trilogy by journalist Stieg Larsson. In November 2004, soon after submitting manuscripts for the first three novels to his publisher, Larsson climbed the stairs to his office as the lift was out of order. When he got to the top, he suffered a fatal heart attack. His books were published posthumously, and have become one of Sweden’s biggest literary exports. By 2019, the series had sold more than 100m copies worldwide.

Journalist David Lagercrantz was commissioned to continue the series, writing three further instalments before Smirnoff took up the mantle. Her book, The Girl in the Eagle’s Talons, translated into English by Sarah Death, inherits Larsson’s beloved main characters: the leather-clad Salander and Mikael Blomkvist, a womanising reporter who works for Millennium, an investigative magazine that – to his dismay – has turned into a podcast.

Sexual violence permeated Larsson’s novels – indeed, the Swedish title for The Girl With the Dragon Tattoo is Men Who Hate Women – and the same can be said for Smirnoff’s latest. Women are subjected to dehumanising violence from the first few pages. “I’m more angry about certain things than men can be,” says Smirnoff. “Because some things you can’t understand as a man.” Yet the writer says she doesn’t like “eternal” victims – she endeavours to transform them into predators, or “at least turn the situation around”. This is something you can’t do in real life, she explains, but you can do in literature. “You can take revenge.”

Upon his death, Larsson’s estate was divided between his father Erland and brother Joakim. His long-term partner, Eva Gabrielsson, had no legal right to inheritance because the pair were not married and Larsson died intestate. In 2015, Gabrielsson said choosing Lagercrantz as the new Millennium author was “totally idiotic”, adding that she “wouldn’t have continued Stieg’s work” herself.

Although Smirnoff has a “good relationship” with Larsson’s family (they sometimes go for dinner), she has not met Gabrielsson. “I haven’t heard anything from Eva of what she thinks today about the continuation of the series,” says Smirnoff. “Since Stieg Larsson’s family, who inherited the rights, have approved, I don’t have a problem.”

In Smirnoff’s continuation, we meet a new character: Svala, Salander’s code-cracking niece. Svala’s mother has gone missing and Salander is called on by social services to look after the 13-year-old – about which the asocial Salander’s first thought is: “Fucking hell!” Smirnoff believes Salander was “like a teenager” in the first six books, and that it was “time for her to grow up”. Though she toyed with the idea of giving her a child or a dog, she eventually settled on the genius niece, an important character who will feature in the eighth and ninth books, which Smirnoff has also been commissioned to write.

Smirnoff worked as a journalist before quitting her job to buy a wood factory, which she still owns. “I decided a few years ago that I had to do something if I didn’t want to work with wood for the rest of my life – and I didn’t.” So once her children were grown up she decided to pursue creative writing, attending a course at Lund University. A year later, in 2018, her first novel, Jag for ner till bror, was published, available in English as My Brother. The thriller, the first in a trilogy, is set in a small village in northern Sweden where dark secrets slowly come to light.

Smirnoff’s publisher thought she would turn down the Millennium offer – she had two books of her own on the go that she had to put aside – but the writer saw it as “an opportunity you never get back”. When Larsson’s family read Smirnoff’s synopsis, they were pleased. “They liked me being a woman, and being from the same area as them,” she says. Smirnoff and Larsson were both born in Västerbotten County, and the new book is set in the northern Swedish wilderness. “Greenwashing”, and the damage caused by ostensibly green companies, is a major theme. “I thought, what would Larsson have written about if he lived today?” says Smirnoff. “Climate change would have been something for him.”

Smirnoff has started writing the eighth book, which is about the mining business. However, she is not going to make a “proper” plan for the novel. “This is a huge project, taking many years, so it has to be fun,” she says. “And it’s a lot more fun to write if I don’t know what’s going to happen.”

• The Girl in the Eagle’s Talons is published by MacLehose Press (£16.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges apply