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.