I have land rover 2012 LR2 116,000 km. when I fill-up the gas tank to the top the engine will shut off if not immediately
after I driving it 2 or 3 kilometres the engine shutoff but itself and will not start until after some cranking attempts or leave it off for 5 minutes and try crank it again

NOTE: The Battery is new



please help

Might be the fuel pressure regulator.

Get a code reader like this one, and pull your codes. That will probably narrow it down.

https://www.harborfreight.com/OBD-II...xoCM9UQAvD_BwE

I am assuming that you don't have keyless ignition.

If you have to insert the key into the slot then please answer the following question.

Do you leave the key docked while fueling?

Otherwise known as "If it hurts, don't do that!"