There are many different circumstances to accepting a student's previous rank. If the style was completely different than I would say, start over because I wouldn't even know the basics. If the style was similar, then the student should be reevaluated to a rank that suits their skill. This was what happened to myself, and I agree with what my instructor did. I caught on quickly, and relearned everything including all patterns, knowledge, self defense... of the ranks beneath, in time to test for the next rank as if I had gone to the school from the start. For a black belt, if they are to keep their rank I would assume that they would know that they have to train hard consistently in order to catch up and understand the new style. Besides, if they join a new style, I assume they are interested in learning and want to train, and with past experience they would be able to catch on easier. In some cases, this might be true, in other cases it's not. And it's quite a shame, not only for the instructor, but the other students who feel pride in their school when someone stops in to watch the class and they notice a "black belt" with skill that would make people wonder what the standard is.