My sister has a sister-through-nursing, so is it permissible for me to marry this sister through-nursing?

It is legally established that the sister of a sister-through-nursing is not considered a sister-through-nursing. So, if your sister had been breast-fed by the mother of that girl, your sister is a sister of that girl through nursing, but this relation through nursing does not extend to you, so you are not her brother-through-nursing and you, thus, are permitted to marry her.

However, if you meant that this girl and your sister had been breast-fed by your mother, then she will be your sister-through-nursing and it is not permissible for you to marry her. This applies when breast-feeding was during the first two years and they were five full feedings.

And Allah knows best.