It is widely accepted that Kanku-sho (originally Kushanku-sho) was created by Anko Itosu, inspired by and complementing Kushanku (Kanku-dai). As to when he did this, it is not known. Did he implement a big revision of the kata, including the creation of the Pinan series, all in one go, or did his deep study of karate see him develop Kusanku-sho and Bassai-sho, for instance, much earlier - or even later? The Pinan (Shotokan's Heian kata) were introduced into the Okinawan school system in the early 1900s, but the period of their actual development is not known.
Sensei Kanazawa mentions that Kanku-sho was preserved by Choshin Chibana, one of Itosu's top students and the main founder of modern Shorin Ryu (Kobayashi). I'm not sure this can be strictly true. For one thing, the kata appears in other lineages that come from Itosu that don't include Chibana. There is also a story that Chibana did not learn Kusanku (dai) until after the Second World War, it being taught to him by his student Katsuya Miyahira (who also learned karate from another of Itosu's disciples, Anbun Tokuda). Although by no means impossible, if true, it would seem odd that he knew Kushanku-sho but not Kushanku-dai.
As for the other lineages, Kushanku-sho appears in Shito Ryu, as taught in Japan by Kenwa Mabuni and on Okinawa by Shinpan Gusukuma, both students of Itosu. It also appears on the syllabus for Shigeru Nakamura's Okinawan Kempo - Nakamura had several teachers, among them students of Itosu as well as Itosu himself.
So Chibana cannot have been the sole preserver of Kushanku-sho. That leads to an interesting question, however, namely how did the kata come into Shotokan - did Gichin Funakoshi, arguably Itosu's most famous student, know it as well?
The evidence suggests that he did, though to what extent is another matter. It does seem as though he knew a larger number of kata in his early teaching career than he later practised in old age when he was more focused on the idea of the 'core fifteen' kata that would become the backbone of Shotokan (which did not include Kanku-sho). The Shotokai claim that Funakoshi learnt over 100 kata in his youth is almost certainly hyperbole, and it is well-known that Funakoshi himself taught that you must know the kata you learn with some depth, and must not hurry to learn them in numbers just for the sake of it.
Funakoshi mentions Kusanku-sho in his second book, Rentan Goshin Karate Jutsu, as early as 1925. Two of his students, Mizuho Mutsu and Nisaburo Miki, show the kata in their 1930 publication, Kempo Gaisetsu (though they had just visited Okinawa, so I can't say if it came from Funakoshi or not). In Karate-do Nyumon (1943) Funakoshi includes Kanku-sho in the list of 27 kata then studied at the Shotokan, which tallies with the information that he taught around 30 kata at Keio, the home of the first university dojo (1924).
There is the possibility that it was Sensei Funakoshi's son, Yoshitaka, that knew the kata rather than his father, although there is no reason to think he did not actually learn it from his father, despite his trips to Okinawa and his also learning from another Itosu student, Chojo Oshiro. We can be fairly certain Yoshitaka practised the kata because there is a photo of him doing the tobi ushiro geri from it (though it could also be from Unsu).
Whatever the truth, Kanku-sho came into Shotokan directly from the style's progenitors. It was not transmitted from Mabuni, as Gojushiho and Nijushiho were, and it did not come from Chibana. It was not a JKA addition as, apart from Funakoshi's credentials with the kata, it also appears in Shotokai (Harada*) and Chidokan (Sasaki) - though it is not in Wado Ryu (Otsuka).
Of course the most interesting part of the kata's history lies buried with Anko Itosu, but we can perhaps get a glimpse of his thinking by studying the kata and comparing it with Kanku-dai. I won't entirely close the chapter on the history of Kanku-sho here, as there may be more to learn ...
In the meantime, here is a picture of Choshin Chibana performing the opening move of Passai in the late 1930s.
* I have since learnt that Harada did not know Kanku-sho until 1967. See blog post here.