Koreeda's After Life is set in a waystation where the souls of the recently deceased are processed before entering heaven. "Heaven," for the film, is a single happy memory from one's life, re-experienced for eternity.
The movie is set in a building resembling a decrepit government social services institution. Every Monday, a new group of recently deceased people check in, and the "social workers" in the lodge explain to each guest their situation. The newly-dead have until Wednesday to identify the single happiest memory. For the rest of the week, the workers at the institution work to design and replicate each person's chosen memory, thereby replicating the single happiest moment of that person's life. This moment is staged and filmed.
At the end of the week, the recently deceased watch the films of their recreated happiest memories in a screening room. As soon as each person sees his or her own memory, he or she vanishes to whatever unknown state of existence lies beyond and takes only that single memory with them.
The story pays most attention to two of the "counselors," Takashi (Arata) and Shiori (Oda). Takashi has been assigned to help an old man, Ichiro (played by Naito Taketoshi), select his memory. Takashi reviews videotape of Ichiro's life and learns that Ichiro had married Takashi's former fiancĂŠe after Takashi had been killed during World War II. Takashi has Ichiro assigned to another counselor, but is still troubled by his memories, causing both him and his quasi-romantic interest Shiori to re-examine their (after-) lives.

Question: When people vanish what do they take with them? 
Answer: Only their happiest moment 
Alternative answer: Their happiest memory.