H marries W1.
W1 had a brother B1.
B1 becomes H's brother in law.
W1 dies.
H marries W2.
W2 has a brother B2 who is now entitled to be called brother in law.
In some sense B1, is still a brother in law but not in the same sense that B2 is. Hence, "former brother in law".

Any better way to say it?