The Ahlswede-Körner (AK) coordination problem with one-sided encoder cooperation is considered. Encoder co-operation refers to communication between the encoders via a finite-capacity one-sided link. For this setting, the coordination capacity region is derived. The optimal coding scheme leverages the link between the encoders to optimally handle the correlation between the sources. Moreover, the scheme incorporates several source coding techniques, such as Wyner-Ziv coding, binning and superposition coding. Furthermore, a dual semi-deterministic broadcast channel (BC) with one-sided cooperative decoders is considered. Transformation principles between the two problems are presented and an achievable rate region for the BC setting is derived. The region of the BC is shown to be dual to the optimal region of the AK problem in the sense that the information measures defining the corner points in both regions coincide. Although the optimality of the achievable region for the semi-deterministic BC setting is yet to be shown, the region is optimal in the fully-deterministic case.