The Genovese family had connections to Billy Hill. Lansky went through the Kray brothers cause they actually had the right people in the right positions at the time with the connections the mob needed, it was Hill that gave one of Lanskys men the contact point for the twins.

"I have this Nightmare. I'm on 5th avenue watching the St. Patrick's Day parade and I have a coronary and nine thousand cops march happily over my body." Chief Sidney Green