Price wanted to teach Ghost a lesson and that's why you were transferred so that Ghost could finally think clearly again.

But ghost was only told that you're gone forever, which is why he assumes you're dead...

Price "Say it: I woke up, I found him, that's all I know" Ghost :"I woke up, I found him, that's all I know" Price "Again" Ghost: "I woke up, I found him, that's all I know" his voice breaks, full of pain and despair "I loved him more than anything..."