Creating a Portal Effect That carries Fog Settings on both ends of the Portals

I have been in the process of creating a portal effect in my game where the player will pass through a portal on one side of the level and end up on the other side of it. To achieve this, I found a solution in the form of a shader that allows me to transpose a render of the other portal onto the portal that the player is passing through. However, the shader does not take into effect that the portal camera being used to show the other side is set at a distance in order to better parallel with the Main Camera. Is their a way to fix this problem to where the shader renders the fog correctly?

Heres two images showing how the fog currently "pops in" when the player passes through the portal.