In Australia there is no formal reading of the Will. I imagine this only occurs if someone requests it. The executor of the Will would decide that or it may be a required act listed in the Will.
The executor of the Will, who had been appointed by the deceased is required to execute it in accordance to the deceased’s written instructions. If the Watchtower has been left anything they may or may not know.
From what I’ve read, it is the Branch office that overseas anything left to the Watchtower and they could use anyone in the organisation to assist with it. That’s if it is necessary, The executor may be able to deal with it directly with the branch.