Pulsates when starts then shuts down after warmed up

Lots of ideas and troubleshooting in the link.

https://www.google.com/search?q=2009+Ford+Super+Duty+6.7+Diesel+Won%27t+start+when+warm

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sounds like you have a fuel pump problem, fuel pumps will usually get hot and then shut off allowing it to sit 30 mins lets the pump cool down allowing it to start pumping, the way you can test it is get a can of starting fluid the next time it quits raise your hood and spray some fluid down into the throttle body and if it starts and then dies it is most likely your fuel pump, hope this helps.

If I crank the motor while it is st ??????? Probably ignition module . When it shuts off check for spark .

Change the fuel filter.
You may have to also change the fuel pump (sounds like it is getting weak) , but the filter is the cheaper/first step in the process.

Replace the starter for the armature is swelled up when hot and biding against the starters fields in there starters casing. Upon cooling off the swelling goes down and the starter is able to operate again. Remember when metal gets hot, it will expand and upon cooling it will shrink back to the normal size. After so long it will quit working from being so deformed from so much abuse

check engine coolant temperature when it gets warmer, or at operating temperature, and verify that the temperature gauge is showing warmed up to operating temperature. If the coolant temperature sensor tells the computer the engine is cold it will over fuel and miss and the engine will die. When cooled down it will run fine until it warms up. Also could be coil if it starts missing after warmed up.

Check fuel pressure when it quits.

i would recheck the ignition module, sound bad to me. make sure that you test the module when hot

check for intake leaks.

usually cars that shut off at slowing to a stop its a sensor. lock up torque converter sensor.