This feels like it can be streamlined. Same concepts, just fewer words.
"A recently returned WWII veteran suffering PTSD struggles with his return to society until he meets a woman who shows him how to be happy."
However, the hook in your original logline is the fact that he uses a piano to cope. Without giving away TOO much more information, perhaps you could define more clearly in the logline how the piano helps him?
In both yours and my version of the logline, we've said that the woman "shows" him how to be happy. This implies that once they meet, he becomes a passive character, which threatens to make the story less interesting. Maybe there could be a clearer way to express this.
Is the PTSD just a character trait, or is it also the central conflict of the film? Because if it's the central conflict, and not just a peripheral obstacle, it's probably worth rewording to clarify. "A recently returned WWII veteran struggles to overcome his PTSD in order to be with the woman he loves."
Also worth noting - I'm not a professional screenwriter, just an enthusiastic amateur, so please only take the above as opinion. Regards.