Great question! Do you mean as an official group of 4 during the main event, or anyone any time? I bet some Dartmouth nordic skiers have blazed that section in the past.
A ski team (alpine) buddy and I did it in 18hrs and change in 2002(?), running as bandits on a year when the course was shortened (no Moosilauke summit) due to storm conditions. My first "ultra." Great trails for running and hallucinating.
I know when I was a student (and participated in the 50 mile hike several times) there was an ultrarunner who did it in 11:xx hours (not sure the minutes). He was a graduate student from outside the US. Wouldn't have beat the 9 hour or so record stated above, but it was one of the faster times that's been put up on that section.
I found a FB post on an alumni page, with a guy stating he did the hike in 9 hrs 45 minutes. I asked if that was from the Green to the Lodge, or did we count the end at the peak of Moosilauke. I have not heard back yet.
My route was not an official FKT attempt, and differed slightly from the routes the students take: I started from the Hanover Co-Op, not the campus, and I ended the hike a little south of the summit where there is a memorial for my friend Chad Denning who died on the mountain in 2014.
That said, the effort took 16hrs and 45 mins. The pace was slightly faster than my 2016 attempt in the fall, but the climb up Glencliff was unimaginably difficult. I had a blast running this and may even do it again. I had a lot of help from friends who joined me at the start and at the end.