Is this sentence correct?
This specific ability to care for others before the need for the other to recall that he is living... too.
Context: this sentence is used to illustrate the meaning of the "caring for others"'s concept.
Caring For Others Concept.
The altruistic ability to care for the well-being of others before "the others" ask for or even realise that they need it.
This is purely an assumption based on the limited meaning I can grasp from your post.