Star Trek V: Final Frontier... Moon Boots

obviously depends on the tech. since artificial gravity and inertial dampening are a key element of star trek ship design, the easiest explanation is that the boots have gravity control systems in the soles, in which case, having them function while inverted would, at its simplest, be a case of them functioning regardless of orientation. at its most complex, it would be a matter of them requiring the software to recognize their orientation, and adjust the output to make them work inverted. another related question would be what the design capacity would likely be, as they were shown to have the power to support 2 people, but as I recall the movie, they required a boos system to enable them to lift 3 people.