Did Digory gave his mother the apple and save his mother's life?

At first he was going to steal an Apple to save her, because the witch tempted him. But he resisted and said no. After giving the Apple to Aslan, he used it to plant a tree to protect Narnia. From that tree grew Apples and Aslan gave one of those to Digory. Unlike the original Apples, it would not provide eternal life, butit did heal his mother when he gave it to her.