Is it permissible for him to marry the daughter of his wife’s sister after she dies

Firstly: 

It is permissible for a man to marry the daughter of his
wife’s sister after his wife dies, because what is haraam is to be married
to the girl and her maternal or paternal aunt at the same time. But as the
maternal aunt has died, what is forbidden no longer applies, which is being
married to her and her maternal aunt at the same time. So there is nothing
wrong with his marrying her in that case. 

It says in Tanqeeh al-Fataawa al-Haamidiyyah (1/111) –
a book of Hanafi fiqh –: 

He was asked about a man whose wife with whom he had
consummated the marriage died, and she had a sister; is it permissible for
him to marry her sister one day after she died? 

Answer: Yes, as it says in al-Khulaasah narrating from
the book al-Asl by Imam Muhammad; and as it says in Mabsoot Sadr
al-Islam, as quoted from him by al-Quhustaani; and as it says in
al-Muheet by Imam as-Sarkhasi… End quote. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked:

Is it permissible for a man to marry the daughter of his
wife’s brother? 

He replied: It is not permissible for a man to marry the
daughter of his wife’s brother if the girl’s paternal aunt is still married
to him, just as it is not permissible either for him to marry the daughter
of his wife’s sister, if her maternal aunt is still married to him, because
the Prophet (blessings and peace of Allah be upon him) forbade a man to be
married to a woman and her paternal aunt at the same time, or to a woman and
her maternal aunt at the same time. 

The scholars (may Allah have mercy on them) were unanimously
agreed that that is forbidden because of this saheeh hadeeth. But if the
paternal or maternal aunt dies or he has divorced her and the ‘iddah has
ended, then there is nothing wrong with him marrying the daughter of her
brother or the daughter of her sister, because in this case he will not be
married to them both at the same time.

End quote from Majmoo‘ Fataawa Ibn Baaz (21/8) 

Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: 

A man married a woman and she bore him children. Now he wants
to marry the daughter of his wife’s sister; is that permissible? 

He replied:

The wife is the maternal aunt of that sister’s daughter, and
the Prophet (blessings and peace of Allah be upon him) said: “(A man) should
not be married to a woman and her paternal aunt, or to a woman and her
maternal aunt, at the same time.” So it is not permissible for him to marry
the daughter of his wife’s sister so long as he is still married to his
wife. But if he divorces her or she dies, and he marries her sister’s
daughter, there is nothing wrong with that. 

End quote from Fataawa Noor ‘ala ad-Darb (19/2)  

And Allah knows best.