Having worked at Pratt & Whitney for many years (now retired) I spent some time working with the engine lube systems, including qualifying the oils for use in specific P&W engines. The 'F' in the mil spec is simply specifying the spec revision. You can be sure that Mobil Jet II is up to the latest spec as well as Aero Shell 500 and 560. I cannot recall an oil that we tested, that was certified to the Mil spec, that did not also meet the P&W spec and get accepted for use in the engines I worked on.