Larry Niven's teleportation networks include energy dumps/reservoirs that technologically compensate for changes in potential energy and vectors. Might Zhodani devices that do the same exist? A knapsack full of either very cold or very hot phase-change material, for example?Of course all of this assumes that potential/kinetic energy is being converted into HEAT. Conservation of Energy can also be preserved by Matter to Energy conversion as well (even 'sort of matter-energy conversion' like when relativistic velocities start affecting mass and the energy required to accelerate it).
Hans