I believe its the case that any owner or director needs to pass the test. Therefore I'd imagine anyone with a shareholding would need to do so. As a result, it might not matter if the shareholding proposed changes from 30% to 60% or whatever, they'd all be held to the same standard.
Additionally I think I'm right in saying (and
@Grumpy Old Man will probably know more on it) that the procedure recently changed so that the EFL have to approve at an earlier stage (I think because of people effectively taking over a club and then failing the test).
So it probably isn't beyond the realms of possibility that KLD might be going through the EFL process, especially as it might take a while with him not being based in Britain, but I'd assume that doesn't mean it can't fall through for an unrelated reason in the mean time