 One-point extension between atomic models

If $M,N$ are infinite atomic models of a complete theory and a finite partial elementary map sends $\bar{a}$ to $\bar{b}$, then for every $c\in M$ there is $d\in N$ extending it by $c\mapsto d$. An isolating formula for $\mathrm{tp}(\bar{a},c)$ supplies $d$. Back-and-forth therefore makes any two countable atomic models isomorphic.