The Mormon historians have the cart before the horse. What happens next is most of those guys end up in America in the 1600s (as the New Sweden colony's first shipments of captives).
They expand and spread.
Due to the lack of zap and buzz in native American amanita muscaria they switch to a local product for a source of religious inspiration ~ it's called peyote. Some congregations may use other drugs as well, but not all use a drug having become more regularized in their practices.
Young Joseph Smith and Oliver Cowdry somehow fall into the hands of the COFB and next thing you know they've seen various spectral images.
There ~ does that take care of the picture?
Note that today most congregations have little understanding of where they came from or how any of this happened, but they do have rules, and the members obey or else. The COFB is most famous for prohibiting members from seeing physicians. They have a very high infant mortality rate.
Up until recently they practiced serial polygamy!
In other words, this "Mormon Offshoot" actually started centuries before the Mormon church was founded.
Maybe there's a different definition of "offshoot"......