The correct answer is (B) will have been living.
The sentence refers to a future point (this July) when an ongoing action (living in Japan) will have been in progress — requiring Future Perfect Continuous tense.
"This July" indicates a specific future time reference. The action (living in Japan for three years) is continuous and will be completed at that future point. Future Perfect Continuous = will have been + V-ing, which is exactly option (B). Options C and D use "would," which is for conditional/reported speech, not future statements.