In previous works, the cognitive interference channel with unidirectional destination cooperation has been studied. In this model, the cognitive receiver acts as a relay of the primary user's message, and its operation is assumed to be strictly causal. In this letter, we study the same channel model with a causal rather than a strictly causal relay, i.e., the relay's transmit symbol depends not only on its past but also on its current received symbol. We propose an outer bound for the discrete memoryless channel, which is later used to compute an outer bound for the Gaussian channel. We also propose an achievable scheme based on instantaneous amplify-and-forward relaying that meets the outer bound in the very strong interference regime. © 2014 IEEE.