No relation.
Why, oh why, did they pick the good name "Henrickson" to portray a Mormon polygamist? It's not a common name, especially spelled this way (no "d"). And it's an Americanization of "Henriksson," a Swedish name. Swedes, historically, have been Lutheran (as am I), not Mormon.
Is this pastor Charles or elder Charles I'm addressing?
Just kidding. What's in a name? Don't worry about it. It's only fiction, although apparently hitting close to the truth.
And I can testify to the truth. We had a polygamist community compound a few miles from our house in Sandy, UT. And you could always tell them when seeing them in stores and restaurants; granny dresses, several women together with a bunch of tots. There was no mistaking the situation.
An employee's grandmother had later become the wife a polygamist. When he died, she was on her own but soon became the wife of another polygamist because she couldn't cope with life on her own...or so the story went from the employee.
There truly are parallel universes out there.
An awful lot of Danes and some Swedes were converted and emigrated to Utah. The Utah Historical Encylopedia says:
Denmark supplied more immigrants to Utah in the nineteenth century than any other country except Great Britain. Most of these Danes--nearly 17,000--were converts to the LDS Church, heeding an urgent millennialistic call to gather to "Zion."
and
The federal census of 1910 showed Utah's Swedish-born population at its peak, with 7,227. In that year, Swedish-Americans and their children in Utah numbered 17,063, or 4.6 percent of the state's population.
The Swedes came mostly from the area near Denmark.
Utah's most famous Swede was radical songwriter Joe Hill (born Joel Hägglund), not a Mormon.
A lot of Mormons look as though they could be of Swedish descent—tall and blond.