Fort Boise, the trading post, operated until about 1855. The military Fort Boise was established in 1863, about 40 miles upriver from where the Hudson’s Bay trading post had been. The town of Boise was established next to the fort the same year.
Fort Hall moved around a little more. It stayed in its original location until 1855, serving first as a fur trading post, then, as the pioneers started streaming through as an important supply stop on the Oregon and California trails. In 1869 and 1870, the first military Fort Hall was built on Lincoln Creek, where it streams into the Blackfoot River. It remained there until 1883 when the barracks moved to Ross Fork Creek, about 25 miles to the west.
To confuse things a bit further, you can now visit the full-scale Fort Hall Replica in Pocatello. It’s not at the original site, but it is worth a visit. And, finally, to muddy the historical waters, there is the town of Fort Hall, which is close to the site of the original trading post.