It is genuine.
From the MOTION:
"II. THE TERRITORIAL LAW 57 AND ITS SIMILARITY TO THE1982 LAW OF THE STATE OF HAWAII
We attach to this new motion for judicial notice a copy of Chapter 57, Vital Statistics, the law concerning these matters as it was in the Territorial laws in question. The statute of the Territory thus attached is from the Revised Laws of the Territory of Hawaii 1955 in Three Volumes as published by the authority of the Territory of Hawaii by the Filmer Brothers Press, 330 Jackson Street, San Francisco, California. These three volumes comprise the statutes of the territory including the acts passed at the regular session of 1955 and the special session of1956 as consolidated, revised and annotated. As can be seen, because we attach italso and request judicial notice thereof, these three volumes of the statutes of the Territory are certified by the chairman of the compilation commission of the Revised Laws of Hawaii 1955 as appointed by the Governor of the Territory of Hawaii under Act 179 of the Session Laws of Hawaii, 1953."
As for weather or not attorney Apuzzo know's yet...I don't know.
I think Apuzzo is aware of this, too. I heard Charles Kerchner (his client in Kerchner v Obama) on a talk radio program saying that the grandmother filed the certificate in Hawaii. With the document you posted, his words now make perfect sense to me.
As you know, I am following the eligibility issue closely. Thanks for your continuing updates. ;)