Transfer learning on new image size

Question

Transfer learning: Take a trained neural network and use it for a new classification task.

When we want to use transfer learning with a convolutional neural network, we don't have to use the same image size as input than the image size used for training. But if we change the input size we will have to re-train fully connected layers. See this post on Stackoverflow.

I don't undertand why changing input shape will not affect convolutional layer weight and why it will affect fully connected layer weights.

Tell me if my question is not understanble.