Fujiwara family is from China, I don't know why Japan suddenly related to her.

Isn't she supposed to be a descendant of the Japanese Fujiwara clan?
The actual Hourai Elixir is a reference to the Chinese legend of the Immortal Island of Penglai (which was known as Hourai in Japan), home to a variety of "eternal" things from rice bowls that never emptied to fruits that granted eternal youth. Legends say that the legendary Chinese alchemist and explorer Xu Fu, who was sent by the First Emperor of China to seek out the elixir of eternal life, ended up in Japan instead and accidentally proclaimed Mount Fuji to be Mount Penglai. But I don't think Fujiwara herself is Chinese. Correct me if I'm wrong.

Adding that from Cage in Lunatic Runagate chapter 4 that Mokou tells Keine the story of how she got the Hourai Elixir by following a group of men sent to the top of Mount Fuji in order to dump the elixir closest to the moon.