A private-equity fund manager was sued by New York’s attorney general for allegedly defrauding investors and secretly funneling millions of dollars to a small broker-dealer he controlled. Laurence G. Allen, the chief executive officer of Nyppex Holdings LLC in Rye Brook, New York, misappropriated more than $13 million to enrich himself and his companies from 2008 to 2018, according to the securities-fraud lawsuit filed Wednesday in Manhattan. Allen used “other people’s savings as his personal piggy bank and as a tool to prop up his failing businesses,” New York Attorney General Letitia James said Thursday in a statement.