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:

readability="17">

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.