The presence of a stellar companion can place constraints on occurrence and orbital evolution of satellites orbiting exoplanets, i.e., exomoons. In this work we revise earlier orbital stability limits for retrograde orbits in the case of a three body system consisting of star-planet-satellite. The latter reads $a_{rm sat}^{rm crit} approx 0.668(1-1.236e_{rm p})$ for $e_p leq 0.8$ in units of the Hill Radius and represents the lower critical orbit as a function of the planetary eccentricity $e_{rm p}$. A similar formula is determined for exomoons hosted by planets in binary star systems, where $e_{rm p}$ is replaced with the components of free and forced eccentricity from secular orbit evolution theory. By exploring the dynamics of putative exomoons in $alpha$ Centauri AB we find that the outer stability limit can be much less than half the Hill Radius due to oscillations in the planetary orbital eccentricity caused by the gravitational interaction with the binary star. We show, furthermore, how the resulting truncation of the outer stability limit can affect the outward tidal migration and potential observability of exomoons through transit timing variations (TTVs). Typical TTV (RMS) amplitudes induced by exomoons in binary systems are $lesssim$10 min and appear more likely for planets orbiting the less massive stellar component. A GitHub repository (saturnaxis/exomoon-in-binaries) is available to reproduce figures.
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