Haku-tsuru means "white crane". From the public evidence available, it appears Bushi Matsumura created at least
one Hakutsuru kata. It is true that there are other Hakutsuru kata
created by others, and some of them were Shuri-te practitioners.
Whether one is to consider these "Matsumura" or not can only be a
subjective conclusion. Everyone has an opinion, so it seems. From the
information publicly available, it appears that the Matsumura family
system was comprised of only what Bushi taught, untouched, without any
additions or changes from later successors or other practitioners. For
example, Soken said, "My uncle only learned from Bushi Matsumura and
only taught me what he had learned." If one takes this statement
literally, then the kata in question was passed down from Bushi. There
is one Hakutsuru kata that Soken Sensei mentioned himself. He said that
"After ten years of training my uncle taught me the most secret kata of
Matsumura-style Shorin-Ryu, the hakutsuru kata..." He said that among
the kata he taught, the "last one is my favorite kata that I
demonstrate - because it is easier to do." There is a Hakutsuru kata in
existence that Hohan Soken allowed to be filmed. The one that he
mentioned in this quote would logically be the one that he demonstrated
in front of the camera. It appears to be an actual kata, not just a
bunch of moves that he threw together for the camera as some suppose.
Whether the katas demonstrated by others are the same kata demonstrated
by Hohan Soken is left to be determined by someone who is up to the
task of comparing them.