In Frankenstein, how did Victor Frankenstein's father help out his old friend's daughter after his (the friend's) death?
I think you are refering to Justine, whose story is related to us in Chapter Six of this excellent novel in one of Elizabeth's letters to Victor. However, it appears that it was Victor's mother that actually had more to do with helping Justine than his father. Note what Elizabeth conveys to us regarding Justine's history:
Madame Moritz, her mother, was a widow with four children, of whom Justine was the third. This girl had always been the favourite of her father; but, through a strange perversity, her mother could not endure her, and after the death of M. Moritz, treated her very ill. My aunt observed this; and, when Justine was twelve years of age, prevailed on her mother to allow her to live at our house.
Thus it is Victor's mother who helps the daughter of Madame Moritz by taking her into the Frankenstein household to be trained as a servant and thereby taking her away from her mother who mistreated her due to the affection she received from her dead father. Justine is of course introduced at this point because of the way the creature will frame her with the death of Victor's younger brother.