I don't know if this "problem" can ever truly be "solved" as there's not really a way to prove there to be a difference between something truly "feeling" emotions compared to faking it convincingly. I have to wonder at what point the difference becomes moot, a sort of Chinese room for emotions. I tend to lean towards solipsism when it comes to this kind of stuff, though. Does the difference actually matter?
I could argue that even people who genuinely feel emotions have, unconsciously, learned to feel them through their interactions with other people. Who can prove to me that emotions are something fundamental to humans and not acquired through culture? In a sense, everyone may as well be faking it.