Complex sentence: Prisyazhnyuk then continued his political career as a member of the United Centre but, according to that party, he had never been a member and had only worked with them on a voluntary basis during the 2010 local elections.
Split into simpler sentences: Prisyazhnyuk then continued his political career as a member of United Centre. But according to that party he had never been a member and only had worked with them on a voluntary basis during the 2010 local elections.