I checked a few different sections of the rules page for clarification. My apologies if I missed it but I know I can move ships with tractor beams and have been told the same can be done for stations. My question is, can I travel in hyper with said station? I would rather not make the 14+ day trip to find out I can only move it around the system it is in.
You can only dock stuff with tractor beams, but you have to be pilot or owner of those stuff you try to tractor in. Works with ships and stations (I managed to tractor LSC into T2 before, harder part was getting it out=P But Zhao did it=D), not sure about vehicles. Though can't say if it still works.
Moons can't fly.
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MSH and Lucrehulks, can tractor in stations and move them, though I don't recall hearing of anyone really doing so. Raises all sorts of questions about undocking the station that I really don't have the answer to >_>