When a person says a prayer, where does the prayer intention go, to be stored as energy?

This energy is stored within the akashic records. This is how the Law of Karma can be astute in assigning meaning, through the intention of all on record, as to motivation and level of responsibility. Because to determine that, the Law of Karma must perceive the level of intention behind an act of wrongdoing, for example, as well as a positive act of loving kindness. And that is how it can sift and sort, and weigh and measure, and return an energy of like intensity in the future to its originator as a reward, or a warning and comeuppance to pressure the individual to address a misalignment and take care of it through healing. Otherwise, that negative message will be repeated over and over again in the future.