He wants to marry the daughter of his sister’s husband

Praise be to Allah.

It is permitted, because she is not one of the mahrams mentioned in the aayah (interpretation of the meaning):

“Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters, your brother’s daughters, your sister’s daughters, your foster mothers who gave you suck, your foster milk suckling sisters…”

[al-Nisaa’ 4:23]

What is listed among these mahrams is “your sister’s daughters”, and the girl – in this case – is not the daughter of your sister. So there is no reason for this marriage to be haraam, either on the grounds of blood, breastfeeding (radaa’ah) or being related by marriage. And Allaah knows best.