I would say the best way to handle it is to just not give the player a choice. Have your player pick it up, and "put it somewhere safe". It doesn't appear in the inventory, and the player pulls it out of their ass whenever it's required for the plot. Other rpgs do that all the time, it doesn't have to be a "omg, i can't throw this thing away" item, but as it is now, they've tried to give the players choices for every little thing, and written themselves into weird corners where SH just pops out of nowhere "tada!!!! box!", which is worse imo.
