The woman was appealing against the UK regulator's refusal to allow her to take her only child's eggs to a US clinic.
Her daughter, who died in 2011, was said to have asked her mother to carry her babies.
The mother lost a High Court case last year, the BBC reported.
She was subsequently granted permission to challenge the decision at the Court of Appeal in London, before a panel of three judges.
But, in the latest legal proceedings, lawyers acting for the mother told the judges she wanted to fulfil her daughter's wishes to carry a child created from her frozen eggs and "raise that child".
The mother's wish is to take the eggs to a clinic in New York to be used with donor sperm.
Richards argued that there was "clear evidence" of what the daughter, known only as 'A', wanted to happen to her eggs after she died, and that "all available evidence" showed she wanted her mother "to have her child after death".
The appeal was opposed by the HFEA, which said it had great sympathy for the parents of the dead daughter, known only as Mr and Mrs M.
The HFEA said: "The law requires us to consider whether there is sufficient evidence of informed consent. After looking at the matter in great detail we decided that there wasn't, a decision which was supported by the High Court last September.
The HFEA said it would now reconsider the case as soon as possible.
