A couple of years ago I was hearing from Catholics serving in African countries, where tribal beliefs and practices include polygamy, that Mormon converts were not required to end their polygamous relationships in order to convert.
So, I asked this same question on a Mormon forum and received no definitive answer. Some LDS members who responded believed polygamy was not allowed anywhere. Others thought that a Mormon convert who had more than one wife would be allowed to remain polygamous. I couldn’t find any official stance at
lds.org.
Historically, the LDS church put out a manifesto, officially ending the practice of polygamy. Within the LDS church itself, at this time, some leaders believed it only applied to Mormons living in the U.S. Polygamous marriages continued to be performed by the LDS church for a few more years after the manifesto, in Mexico and Canada. When pushed on the issue, by the U.S. federal govt., they issued a second manifesto that declared polygamy in the Mormon church could not be practiced anywhere.
The existing polygamous relationships continued until all parties involved had died. Because of this, I suspect that polygamous Mormon converts outside of the U.S. continue in their polygamous relationships, but cannot enter into any more marriages than they have/had at the time of their conversion to Mormonism.