If you can ask your boyfriend to take the rabbits to the new place and set up an area for them 1st, that should help them settle. A quiet zone where they have familiar things around them. So their cages or pens set up the same as you have them now. There’s going to be new smells and sounds that they;re going to have to become familiar with, so it’s important they feel they’re in a “safe-zone”. Too much freedom in a new space would be overwhelming and frightening. Even when he gets there initially, he could leave them in their carriers for an hour to acclimatise.
For your own piece of mind, be sure your bf understands the way they are contained is super-duper secure. So they can’t jump out or break free of a cage etc. There’ll be a lot coming and going and doors left open etc. I imagine he’d ensure this anyway but it never hurts to go over these things…
I hope it all goes well! As ChaCha says, they will adjust.