Complex sentence: After the Continuation War, and while still in prison, Tanner became the virtual leader of a faction of the SDP which had strong support from the USA, this faction eventually came out on top after much internal party strife lasting much of the 1940s.
Split into simpler sentences: After the Continuation War, and while still in prison, Tanner became the virtual leader of a faction of the SDP which had strong support from the USA. This faction eventually came out on top after a great deal internal party strife lasting for much of the 1940s.