How do I transfer my service to another computer?

So, I have the Surface by Microsoft, and I have to replace it because the screen keeps flickering whenever it overheats (it has happened to so many Surface users that its been referred to as "Flickergate"). Allegedly, Microsoft will replace flickering surfaces for free within three years of having bought it, so I'm going to call them later to see if that's true. Until then, I want to know if it's possible to transfer my current Adobe Cloud subscription onto my replacement Surface without having to purchase a new one.