By Paul Carsten BEIJING (Reuters) – Apple Inc is finally launching its iPhone on China Mobile Ltds vast network on Friday, opening the door to the worlds largest carriers 763 million subscribers and giving its China sales a short-term jolt. Underlining how much the launch means for Apple, Chief Executive Tim Cook was on hand as the carriers flagship store opened in Beijings financial district. With China Mobile Chairman Xi Guohua alongside, Cook gifted signed iPhones to a handful of customers and posed for pictures. The long-awaited deal could trigger a limited turnaround for Apple, whose fortunes have wavered in China in the face of stiff competition from market-leader Samsung Electronics Co Ltd and up-and-coming local rival Xiaomi Tech.