A submersible pump gas separator for a well pump has a housing with a rotatable shaft. A separating section in the housing separates heavier well fluid components into an area radially outward from the lighter components. A crossover member rotates with the shaft. The crossover member has a helical liquid passage having an inlet in fluid communication with the separating section for receiving the heavier components and an outlet in fluid communication with a liquid outlet of the housing. The crossover has a gas passage having an inlet in fluid communication with the separating section for receiving the lighter components and an outlet in fluid communication with a gas outlet of the housing.