Destination memory can be defined as the capacity to remember to whom we transmit information. It is measured through the accuracy of retrieving the association between the information we transmit and the person to whom we transmit it. A destination memory procedure aims to emulate human interaction by sharing facts with celebrities (i.e., familiar faces) since we often communicate with people we know. However, the role of the choice about who we intend to transmit the information to has not been evaluated before. This paper investigated whether deciding with whom to share a piece of information benefits destination memory. We designed two experiments with different levels of cognitive load, increasing it from Experiment 1 to Experiment 2. The experiments included two conditions: the choice condition, in which participants chose from two options to whom they desired to share a fact, and the no-choice condition, in which participants simply shared facts with celebrities without the possibility of a choice. Experiment 1 suggested that a choice component did not affect destination memory. However, when in Experiment 2 we raised the cognitive load by increasing the number of stimuli, we found that selecting the recipient during the more challenging task provided an advantage in destination memory. This result is congruent with the explanation that the shift of the participants’ attentional resources to the recipient, caused by the choice component, leads to a destination memory improvement. In sum, it seems that a choice component can improve destination memory only under demanding attentional conditions.