So, if you believe that, why do you think he chose to keep about $13 in his possession? The equivalent of nearly 2 days pay. Why not just leave it all to Marina and the kids?
I said eventually, which is ambiguous with regard to how much time might elapse before he is captured or killed. In the meanwhile LHO, if he managed to escape the immediate area, would need cash to get around, eat, etc.. The encounter with JD Tippit helped to hasten the apprehension. And he had already paid for the bus fare and cab ride. So he must have actually kept a little more than thirteen bucks.