The thing about hedgehogs is that their home range and their knowledge of it is very important to them, from good places to find food and drink, to places to rest during Summer days and suitable places to hibernate. If they were to be translocated elsewhere it would be extremely stressful to them, they would be disoriented and they might not survive. Also if you moved the boxes you risk arousing the hogs from hibernation which would waste their store of fat which they need for the rest of hibernation and for eventually coming out of hibernation.
So, if hogs are using the boxes, I think you have to leave them where they are and where they know, if at all possible – in their own familiar range. Perhaps you can explain things to your landlord – give as much information as you can and explain that it is vital that the hog houses need to be left undisturbed until after the end of hibernation. You could also explain how rare hedgehogs have become, how helpful they are to have in gardens, etc. You never know, your landlord may surprise you. If your landlord knows about them, it may be less likely they are disturbed than if you didn’t mention it. I think you need to have the discussion.
If the landlord is definite that he/she is going to evict the hogs, then maybe a local rescue could help (so that the hogs could be released back into the territory they know later on). But I would try to go into the conversation hoping that she/he will want to be helpful to the hogs. If you are leaving any information for your successors in the property, you might consider leaving some information about the hedgehogs, (the presence of the hog boxes, if they want to feed what to offer, the importance of offering water, etc.) amongst them, so that they have the opportunity of becoming interested in the hogs as well.
Tricky situation and maybe not want you want to hear, but sometimes we need to trust that other people may more sympathetic to hedgehogs than we fear.
There is one other thing, though. It’s possible that the hogs may just about be out of hibernation by the time you move – especially if they are males which tend to go into and come out of hibernation earlier. Some do emerge in early March. If you know when the hogs went into hibernation and if it was early – say September – they may emerge earlier – although it isn’t an exact science. So whilst I would have the conversation with your landlord earlier (so that you are prepared for whatever eventuality), if, as a very last resort, ‘rescuing’ does become necessary, I would leave that as late as possible so that the hogs have every chance of emerging from hibernation naturally. That sounds as if it would be the best case scenario.
Good luck to you and the hogs. I hope your move goes well.