of course we’re now over analyzing w/o all the details but being they were only 10 feet above him you could just lower a locker on a overhand on a bight if you have no free ends. I “think” she probably put him on a plate device off her harness, but then there was some more adjusting going on as they were telling the climber to wait.
TBH, just lowering a locker and fixing the rope instead of belaying probably would have been a little better and less time consuming... then he could just batman the 15 feet up to the anchor (once he put his tools away). Especially since the climbable ice was disappearing...
Disclaimer: this is over thinking something that went down very fast and was handled well. It is not meant to cast any judgement, just reflection on other ways to handle a similar situation.