Happy lies about Biff, but does not say that Biff has been in the war.
The actual line in the play has Happy lamenting the fact that he was not accepted into the armed forces himself. He goes on to say that Biff is back and has returned from the west.
Stanley: Oh, he came back, heh? From the Far West?
Happy: Yeah, big cattle man, my brother, so treat him right. And my father's coming too.
Biff, of course, is not a "big cattle man". He merely works as a laborer on a ranch. Happy's willingness to lie and bend the truth is on display here as it is through much of the scene. Happy lies to the woman who he meets and encourages Biff to lie to Willy about how the meeting with Oliver went.
Happy suffers no compunction when it comes to lying. He is quick and willing with a lie, but he does not say that Biff has been in the war.