The 'inheritor' of a will is irrelevant here. It's the executor of that will who is responsible for sorting out the estate of the deceased person and who therefore (quite reasonably it would seem to me) has the right to receive correspondence addressed to the deceased person. (For example, they'll need to know about any bills, or other demands for payment, that have been sent to the deceased person).
So who is named as the executor (or joint executor) of the will?