Someone suggested above that you need a fixed multi camera rig to do that easily. That way you are sure the object and the cameras is in the exact same position when you project the images. As you don´t have that it will be more difficult. You do have some options though but they are more advanced. I have not tried his but you could duplicate the chunk with the non covered cup and then import the covered cup mesh in to that chunk. The Cup will probably be the wrong scale and position. You then have to manually scale and move it until it matchs the original cup position of the un covered cup. Not sure if this can be done in standard version but i think it can be done in the pro version. You then build thexture and select keep UV.
Other options are manually texturing the cup in a 3D modeling program using your images of the un covered cup as reference. If you have some skill you can get an accurate result. I would use Zbrush´s spotlight for this. It must be a very unique cup for it to be worth it though
I guess yoo are only using the cup as a practise object right?