The coupe was my first new electric in ages, and I loved the look of the Epiphone cases.
Ironically, I went through the same curiosity as you did, since it wasn’t made clear anywhere.
I have owned both the coupe and the case for a little over three years. Good morning - I only just saw this post, so forgive me if it has been a while, but, yes, the 339 case will fit.