Oh, my. I assume you must mean Green Park, the route already posted by Globaliser. As a user of the bottom end of the Jubilee, ‘ never change at Green Park’ is a personal rule, but if you must, follow G’s first suggestion, the ‘Way Out’ route…
Well, it’s a darn sight closer than LHR 🤣 My preferred route would actually be train to Paddington, then Bakerloo and Jubilee lines, using the easy level change at Baker Street. I accept the added expense to avoid the interminable Piccadilly leg to Heathrow (which I have done dozens of times), but I am in a minority on this board! Doesn’t matter to the OP, of course, given the rail strike.