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In this article, we study the uniqueness and nondegeneracy of ground statesto a fractional Choquard equation of the form: $(-\Delta)^su+u=2(I_2\staru^2)u$ where $s\in(0,1)$ is sufficiently close to $1$. Our method is to make acontinuation argument with respect to the power $s\in(0,1)$ appearing in$(-\Delta)^s$. This approach is based on [M. M. Fall and E. Valdinoci, Comm.Math. Phys., 329 (2014) 383-404].

Uniqueness and nondegeneracy of ground states for $(-\Delta)^su+u=2(I_2\star u^2)u$ in $\mathbb{R}^N$ when $s$ is close to 1