So, Schmidt has realized, maybe just for a moment, that it is not "about Schmidt." His depression changes, if only briefly, to joy. And the reason? A little boy, many thousands of miles away, has loved him. Sure, Schmidt sends the money that makes the boy's life a little bit better, but you sense that it is the letters that he loves. Schmidt, of course, has been using these letters as an opportunity to vent on his own issues and to dispense ridiculous advice (at one point, he suggests that Ndugu save some of this money for college), not to build a relationship with the child.
The relationship between Schmidt and Ndugu is one-way. At first, it's from Schmidt to Ndugu, and Schmidt is unmoved. But when that changes, when Schmidt feels Ndugu's one-way love in a moment of need, he is reborn. It is when we are loved that everything changes. Like Schmidt, who appreciates one-way love that comes when he hits bottom, it is when we feel that no one could possibly love us that we are most eager for a God who says, "I came to love the unlovable."