Getting materials and working on technical execution

After visiting many supermarkets and department stores, I couldn't find any paper cups with a large size, so I went to Chatime and asked to them if I could buy one of their empty coffee cups. After that I tried to figure out how to make the pop-out image work based on the mechanics of pop-up slider cards. Unfortunately my attempt didn't work and this was my outcome:

I decided to stick a paper between the pop-out image and the cup holder so the effect of the pop-out will work more. I would also be slideable up and down. However, it does not look good presentation-wise because of the paper sticking out from the bottom. Ms Anis suggested to use a different approach: where the user themselves push the pop-out image back in so the cup holder can be slid back into place.