Hutch and run connections help sugguestions please

We are not far off moving the rabbits into their new play house but need to figure out the best way to let them have access from the play house into the run. There is a 5mm gap between the two and not sure the safest way to add a connection.
I don't have room to make this gap between the two any bigger as if I did I would add a run around pipe.

Help any ideas please?

Thanks

With a gap that tiny, you could simply cut a hole in each and let them hop through, it doesn't need a tunnel. If you wanted one or the ability to close it off, you could look at the cat flaps designed for extra thick doors/walls.

Thank you