As I understand it, you have an aerial whose lead terminates in a socket near your fireplace. An extension, with in-line amplifier has been routed externally so that you have a Freeview box adjacent to your TV in another room.
You now wish to have a Freesat box also adjacent to your TV. It seems that you have a satellite cable terminated in some manner near your fireplace. I don't understand what you mean by "the inbound satellite/freeview box". Does it contain a Freesat receiver? Can you provide make/model details? I suspect that you will need to run a cable for Freesat, using F connectors, in the same manner as has been done for your aerial, possibly by-passsing the "satellite/freeview box".