I think what the theory embodied cognition tries to point out is that strong AI is not this cognitive "thing" that can be transferred from container to containe

I think what the theory embodied cognition tries to point out is that strong AI is not this cognitive "thing" that can be transferred from container to container. Imagine that we discovered that Dolphins were just as smart as us and also imagine aliens discovered us, embodied cognition says that the cognitive apparatuses in each of these and us is radically different because brains are always wired up to bodies. It's not that AI needs to be embodied (computation and cognition are always housed in something), it's that what the housing is will affect the AI. In other words, don't think that strong AI means "thinking like a human" because that AI won't have a human body. At least that my take on it.