How could Jeremy remove the silencer after he shot and killed Sheila, and take the silencer all the way downstairs by either route, and hide it in a box at the back of the gun cupboard in the downstairs office?
He could have gone into the bathroom on the upper floor, then unfastened the door from there into the rear storeroom, and proceeded via that storeroom into the upstairs office. From there, he could descend the back stairs and go into the rear laundry room where the gun cupboard was. He could then return upstairs by the same route (in reverse), locking the storeroom door and securing the door from the bathroom behind him. Finally, he could go downstairs via the main staircase (or via the kitchen stairs) and exit the building via a ground floor window that could be caused to latch from the outside. Note that this route also explains how the rear storeroom was locked from the inside. I doubt that this happened, but it is a possible route.
What seems highly implausible is for the murderer to have escaped via the skylight, as he would have had to leave the house (as described above) and re-enter the building to do so, having left two doors unlocked to make this re-entry possible. Such re-entry would have served no purpose.
I think Campion was mistaken in asserting that the back door key was missing. Instead, the back door was found locked with the key in the lock.
