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

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.