When Lee Kun-hee, the patriarch behind Samsung Electronics, died in 2020, his dynasty soon dealt with a crisis on two fronts: first, a multibillion-dollar inheritance tax. The following year, his son Jay Y. Lee was jailed after being convicted of bribing South Korea’s former president Park Geun-hye to win support for his succession.At the time, some observers speculated that the sheer scale of one of the world’s largest death levies could threaten the family’s control over the conglomerate.Instead, more than five years later, an AI-driven upswing in semiconductor valuations has helped the family cement its grip and grow richer than ever. The Lees’ combined wealth climbed to about US$45.5 billion as of March, from roughly US$20.1 billion a year earlier, according to the Bloomberg Billionaires Index.They are now Asia’s third-richest family, up from 10th last year. The heirs are set to complete the final instalment of their 12 trillion won (US$8.1 billion) inheritance tax due this month, wrapping up about five years of payments.A spokesperson for the National Tax Service declined to comment. Samsung is the biggest of South Korea’s family-run conglomerates known as chaebol, alongside SK Group and Hyundai Motor Group.Jay Y. Lee, who once shunned the limelight as his sentencing drama roiled South Korea, is back. Last week, he appeared in a selfie with the nation’s President Lee Jae Myung and India’s Prime Minister Narendra Modi during a visit to New Delhi. Over the past year, he joined presidential trips to India, Vietnam, China, the United Arab Emirates and the US.