Deriving The results of the recent paper on Conformal BMS group

Question

In a recent paper (here) by Hawking, Malcolm and others they have described conformal BMS group. This is an extension of the BMS group as was already known. I am trying to rederive these results but can't do that. Can anyone suggest a good way to tackle the problem? I am particularly intersrested in deriving 4.1. Thanks.