Later, they may wish they had paid more attention to their parents precious memories.
The correct option is later because it expresses contrast and time lapse between the two ideas. On the first hand, when the inmigrants' children are young they do not worry about their ethnical origin, or about old family stories, but later they regret not having listened to those, because they end up developing an interest on them, and maybe is too late then because older family generations might not be there anymore.
Using therefore, would not make sense, because it connects the two ideas providing the meaning that the second (they may wish they had paid more attention to their parents precious memories) is a consequence of the first (they often do not want to hear about life in the old country).