Genjii was Reimu's flying aid from Touhou 2 through 5. Between Mystic Square and Embodiment of Scarlet Devil, though, she learned how to fly by herself. No one has seen or heard anything of Genjii since then, but it's safe to assume that he's now living a peaceful life at the Hakurei Shrine. He is "probably living in the lake at the back of the shrine" according to ZUN.
In Strange and Bright Nature Deity Chapter 12, Reimu and Marisa have a talk about Glowing Moss. Reimu said it would be nice to transfer it to the pond in the back of the Shrine and Marisa responds that she could make it grow there on the turtles' backs. Even if it was more than one turtle, it could refer to Genjii.