The terms "post human" and hyperspace are unrelated.
Post human relers to the state where either humans have been replaced by something supreior, or a situatoin where humans have evolved into a non-human form. We have much of the science to be able to do this now, we just don't have the technology. My guestimate is that we will have such technology in under a century.
There is currently no indication that the concept of hyperspace will ever be accessible to any form of technology that we can ever develop. Whilst technology can still make enormous progress, there is no indication that there is any more significant new physics to discover. Therefore assuming that hyperspace even exists, there is no reason to believe we can ever utilise it for anything.
Cheers!
