When Koo Bon-moo, chairman of South Korean conglomerate LG, died in 2018, there wasn’t much question, at least publicly, of who would next preside over the company.LG, a $10 billion corporate empire, is governed by the principle of male primogeniture. Succession was effectively settled 14 years earlier when Mr. Koo and his wife adopted their eldest nephew, Koo Kwang-mo. The adoption was necessitated by tragedy and tradition after the couple’s teenage son died in 1994, and their efforts for another male heir resulted in a second daughter.The Koo family has controlled LG since it was founded in 1947, and the transition that elevated Kwang-mo to the helm seemed seamless, burnishing the family’s reputation for harmony.It wasn’t.The former chairman died, at age 73, without a will. What followed was a power struggle within the Koo family and LG over the inheritance of his estimated $1.5 billion fortune — including his 11 percent stake in the company. Now, five years later, the former chairman’s widow and two daughters are suing Koo Kwang-mo, accusing him and other LG executives of deception to steal their rightful inheritance to bolster his claim to the company.The women said they want their full inheritance, but they are not seeking control of LG.The lawsuit not only pits the matriarch of one of South Korea’s wealthiest families and her daughters against the adopted male heir, who is now one of the country’s most influential business figures. It also challenges LG’s patriarchal tradition that allows the oldest male successor to seize power and wealth, leaving female family members as afterthoughts in the company.Omnipresent in South Korea, LG is a holding company comprising 11 publicly traded businesses, including LG Chem, the country’s largest materials and chemicals firm, and LG Electronics, whose televisions, dishwashers and other home appliances are popular worldwide.The Koo family is one of a few wealthy clans — along with the Lee family at Samsung, Hyundai’s Chung family and SK’s Chey family — who run the conglomerates known as chaebols that have dominated South Korea’s economy for decades.In a legal filing that reads like a Korean drama script involving one of the country’s biggest corporate employers, the former chairman’s widow, Kim Young-shik, and her daughters, Koo Yeon-kyung and Koo Yeon-sue, accused LG executives of colluding with Koo Kwang-mo and his biological father to swindle them.In transcripts of secretly recorded conversations filed in the legal documents, Koo Kwang-mo pleads with his adopted mother not to challenge the inheritance because it will hurt LG’s image and his leadership of the company, potentially tarnishing his reputation among the Korean public.“The scariest thing is the public opinion,” he said, according to the transcript. “How are they going to look at this situation? ‘Someone got greedy,’ or that I didn’t come visit and do a good job of caring for my mother.”In addition, the women accused Ha Beom-jong, the former chairman’s aide and now LG’s president, of misleading them to believe that there was a will that left everything to Koo Kwang-mo. Without a will, South Korean law states, the widow would be entitled to inherit one-third of the estate with the remainder divided equally between the two daughters and Kwang-mo.Instead, the women said they were duped into an agreement in which roughly 75 percent of the estate went to Kwang-mo. The lawsuit, filed in Seoul Western District Court, seeks to redistribute the estate according to the legal standard.“We cannot stand having our rights, protected under the constitution and the law, be disregarded just because we are women,” the women said in a notice filed with the lawsuit.Yulchon LLC, a law firm representing Kwang-mo, said in a statement that the inheritance is “a legally settled matter” that was resolved four years ago after extensive negotiations, and that there have been about 10 rounds of consultations and several revisions since the chairman’s death. It also noted Ms. Kim had signed a document agreeing that Kwang-mo should receive the LG shares and assets related to controlling the company.While LG is not a party to the lawsuit, it has also staged a vigorous defense of Kwang-mo in public statements. LG also suggested that the women were trying to challenge Koo Kwang-mo for company control, something that they deny.“Any attempt to shake LG’s tradition and management rights cannot be tolerated,” the company said in a statement earlier this year.