Is it permissible to do a Caesarian for a woman who has died but there is a living foetus in her womb?

If a woman dies with a foetus in her womb, and there is the
hope that he will live if he is taken out without doing a Caesarian, then
he has to be taken out. If it is not possible to take him out except by
doing a Caesarian, it is permissible to do that so as to save his life.
But if there is no hope that he will live, it is not permissible to do the
Caesarian because there is no benefit in doing it; rather he should be
buried with his mother without the operation. 

Al-Nawawi (may Allah have mercy on him) said: If a woman dies
with a living foetus inside her, our companions said that if there is the
hope that he will live, her stomach may be cut so that he may be taken out,
then she may be buried. But if there is no hope that he will live, there are
three points of view, but the correct view is that her stomach should not be
cut; rather it should be left until he (the foetus) dies, then she may be
buried. 

End quote from Rawdat al-Taalibeen, 2/143 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
This is the correct view especially nowadays when taking out the foetus is
not regarded as mutilation. If a woman dies with a moving foetus in her
womb, the operation should be done straight away and the foetus taken out,
and this is not mutilation at all.

End quote from Sharh al-Kaafi. 

He also said: 

If there is a need for surgery, there are four scenarios…

The fourth scenario is where the mother is dead and the
foetus is alive. If there is no hope that he will live, then it is not
permissible to do the operation. But if there is the hope that he will live,
if he has partially emerged then the mother’s stomach may be cut so as to
take out the rest of him. If he has not emerged at all, then our companions
(may Allah have mercy on them) said that the mother’s stomach should not be
cut in order to take out the foetus, because this is mutilation. But the
correct view is that the stomach should be cut if he cannot be taken out
without doing so. This is the view favoured by Ibn Hubayrah who said in
al-Insaaf that it is more correct. End quote from Majmoo‘ al-Fataawa,
11/333 

And Allah knows best.