I’m glad that helped you, but if you want to have some control over the shadows of the glass, since my method is a bit darker in that area, cause it doesn’t use so many glossy bounces, you could also increase a bit the glossy bounces or you can use another mix shader node this way and control the intensity of the shadow with the color of the transparent material.
Here:
This way you can use the color of the second transparent material to control the shadows as you wish.