Final answer:
Britain set up the Hudson's Bay Company by obtaining a Royal Charter from King Charles II in 1670, granting a trading monopoly in Rupert's Land.
Step-by-step explanation:
The Hudson's Bay Company was established by Britain through negotiations with English King Charles II and the subsequent issuance of the Royal Charter in 1670. The company was granted a trading monopoly over the watershed of all rivers and streams flowing into Hudson Bay, an area known as Rupert's Land.
The establishment was not achieved by conquering French fur trading posts, forming alliances with French fur traders, or establishing military outposts, but rather through the legal grant of trading privileges over a vast area.