Currently, Thomas Monson is the prophet. He does lead the church under Christ. But there is a bit more to the authority than that. Thomas Monson leads the church under Joseph Smith, who remains the head of this dispensation beyond the veil. Joseph Smith still leads the church. He still leads it under Adam, who is the ancient of days, is Michael the archangel. Michael led the saints in the premortal world and he continues to lead them in this world. And when Satan is cast out of this world it will likely be just as true as it was in the premortal life that it was done with Michael the archangel at their head.
And who does Michael lead the saints under?
Why Michael leads it under Christ.
So yes, this is the true Church of Jesus Christ. Yes, he is the head of it. President Monson leads the church under Christ. But there is nothing wrong with acknowledging the whole chain of authority and realizing that President Monson leads it under Joseph Smith who leads it under Adam who leads it under Christ.