The ensemble Kalman sampler (EKS) is a method introduced in [Garbuno-Inigo et al., SIAM J. Appl. Dyn. Syst., 19 (2020), pp. 412--441] to find approximately independent and identically distributed samples from target distribution. As of today, why the algorithm works how it converges mostly unknown. continuous version set coupled stochastic differential equations (SDEs). In this paper, we prove ...