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We should care about all life. If life continues after death, then we should care about that too.
There is no scientific knowledge as to what happens after death.
Through technology, we might just be able to create it.
Many people use that act of caring (their "beliefs", if you will) to encourage them to continue their life BEFORE death.
If by "life after death" you mean a continued existence after one's body dies, then I think the only way we can "care" about it is by trying to figure out what that would be exactly. Figuring this out could lead to a deeper understanding of ourselves. What would persist is, in itself, interesting.
We should care about life after love
because even if it were true, it causes us to devalue the opportunity, challenges, and life we know to exist. Life after death serving as an incentive for good human behavior is not the most noble reason to be good.