A partnership Rudy Giuliani forged with a wealthy diamond-trading family from Israel helped his effort to expand his fledgling consulting business in Japan, and generated more than $600,000 in speaking fees for the Republican presidential candidate. The former New York mayor's previously undisclosed relationship with the Sage Capital Growth -- a medium-size private equity firm associated with the diamond-trading Steinmetz family of Israel -- shows how money came his way after he earned international acclaim leading the city through the Sept. 11, 2001 terrorist attacks. It offers a peek at Mr. Giuliani's closely held five-year-old consulting business, New York-based Giuliani...