Her name was Rosa, too--but truly she was Rosa, first. Her husband thought it too beautiful a name, thought it should go on and on, named their daughter after her mother. The daughter looks like the mother (Mr. Grewgious peers at her in the firelight as she watches him, too, a little shy, a little too childish and self-righteous to be shy). The daughter, when she grows a little, will smile like her mother. It already hints at her mouth when she is pleased; he's seen it.
Mr. Grewgious peers at her in the firelight, and for a moment the flicker makes her look just like Rosa, because the parts in shadow are the daughter, the parts lit up are her mother. He agrees to help her without hesitation.

That, my dear, is called I-haven't-read-the-book-in-ages-and-I'm-trying-to-write-about-a-scene-I-don't remember, but there you are.