Hello, sorry for the length of this comment and if all of this is already known. I found this post and the articles most intriguing and wanted to contribute.
I looked around in old Swedish newspapers and this is what I found.
Only according to this papers, not taken for actual facts, he should have been born in Stockholm 1791 as the son of a poor potter. He went to sea as a 12-year old and emigrated in 1807, at the age of 16. He married the daughter of a Chippewa chief, had nine children and died around 1871 about 80 years old, presumably at his home near Afton in Washington county.
I have translated the texts from Swedish with the aid of google so excuse me for possible mistakes. The language in some of the articles are not politically correct nowadays in Sweden or, as I presume, elsewhere but I have kept it as it was written.
Svenska Dagbladet 1983-12-13
“Minnesota in the early 1850s In a letter, the aforementioned Norberg tells about Jacob Fahlström born in Stockholm in 1791 He went to sea as a 12-year-old ...”
https://tidningar.kb.se/1767385/1983-12-13/edition/0/part/1/page/12/?q=%22jacob%20fahlstr%C3%B6m%22%20minnesota
Dagens Nyheter 1984-09-28
From a book review written by Kjell A Johansson about the book "De första utvandrarna" by Alf Åberg
The destinies that stick in the memory are instead those that deviate from the pattern, for example the first Swede in Minnesota, Jacob Fahlström from Stockholm. He early married an Indian girl who was the daughter of a Chippewa chief, had nine children with her, lived a free and successful life and aroused the admiration of the first Swedes who eventually came to the area. Today, descendants of Jacob Fahlström are probably scattered over a large part of the United States.
https://arkivet.dn.se/sok?q=%22jacob%20fahlstr%C3%B6m%22%20minnesota&from=1864-12-23&sort=newest&to=2020-12-31
From response by Vilhelm Moberg to an article by Göran Lindahl in Dagens Nyheter 1958-07-27
"The Story of the Emigrants"
"We have here, for example, Jacob Fahlström, called 'the first Swede in Minnesota', a legendary figure in this state. He emigrated in 1807. He was the son of a poor potter in Stockholm and therefore came from 'the broad folk layers'. If Lindahl had happened to read about Fahlström in my book "Den okända släkten" (1951), he would of course have left a completely correct information here."
https://arkivet.dn.se/sok?q=%22jacob%20fahlstr%C3%B6m%22%20minnesota&from=1864-12-23&sort=newest&to=2020-12-31
From Södermanland's Läns Tidning, No. 9, Wednesday, February 2, 1881.
“Among the redskins of North America.
In a small booklet printed in America about the Swedes in Minnesota, the following curious description appears: A Swede, who lived among the redskins around Lake Superior and St. Croix river, long before any other white man put down his stakes there, was Jacob Fahlström. About this Fahlström it is said that he would have been born in Stockholm or the surrounding area. At the age of 12, he accompanied an uncle to England. From here he must have sailed as a sailor for some time until we find him at Hudson Bay, where he learns to have worked for the company of the same name. During his stay at Hudson Bay, Falström got lost during a hunt. After several days of wandering in the forest, he was taken in, exhausted and starving, by a pack of Indians, of what tribe we do not know. He now accompanied these Indians for a long time. After countless hikes and wanderings in the great forests, Falström and his companions arrived near Lake Superior. Here they got into a fight with a detachment of Chippewa Indians, who won and captured both Falström and part of the foreign Indian tribe. The victors released their red prisoners, but Falström remained among the Chippewa tribe. Here he married a squaw, half negro and half Indian, and lived with these redskins for a period of 25 years. During this time, Falström happened to get lost on the hunt another time. He then wandered about in the forest for eighteen days without food and without encountering any human being. His ammunition had run out, and he had to survive on wild roots and rotten fish, which he found floating about the shores of the lakes he passed. After many years of living among the redskins, Falström finally came into contact with white people again. In the vicinity of St. Croix river, he again met his countrymen, the Swedes. He had almost completely forgotten his mother's language, but practiced and learned again during conversations and socializing with them in his childhood language. He took up land and settled near Afton in Washington county, where his sons still live. In the later years of his life, Falström became deeply religious and showed great fear of God and worked seriously and with zeal for the spread of God's word among the Chippewaindians, among whom he acted as a missionary. He also used to hold prayer meetings with the newly arrived Swedish settlers, but his language was then a mixture of Swedish and English, often quite difficult for his listeners to understand. He was very unassuming and did not wish to attract much attention. On entering some strange house he took his place in some hidden corner by the door. If, as often happened, he was addressed by his countrymen with the word master, he replied: "I am not a master, there is only one master, and he is". pointing upwards, "lives above us". Falström died about 10 years ago and is said to have been about 80 years old at the time of his death”
https://tidningar.kb.se/2822409/1881-02-02/edition/170081/part/1/page/4/?q=%22jacob%20fahlstr%C3%B6m%22%20minnesota