At one point, Morgan served in the Israeli army.She later quipped that the reason she left Israel was that she "couldn't make enough money to pay for [her] bras." In fact, Morgan met Joseph Wilczkowski-- an American tourist and survivor of the Holocaust-- in the late 1950s. The two were married ten days after their first meeting and moved to the U.S. where Morgan and Wilczkowski lived a happy life together for over five years. Morgan recalled, "It worked perfectly."
By 1965, Morgan and Wilczkowski had two daughters, and Wilczkowski was a co-owner of two meat markets in the Bedford-Stuyvesant section of Brooklyn. Wilczkowski operated the smaller of the two markets, which were across the street from each other. On Sunday, March 27, 1965, Wilczkowski, his partner and an employee were killed in a brutal robbery that grabbed national headlines and became known as the "icebox murders".