This is not the Knights Templar with which I am slightly familiar. There is a degree of York Rite Masonry known as Kinghts Templar.

Masonic Templars do not claim direct relation to the Templars of old. However when the Knights Templar re-emereged in the early 1700's, the Order was a part of Freemasonry.

Membership in the Order of Knights Templar is limited to Christians who are hold higher level degrees in York Rite Masonry.

I can not, and will not speculate as to which body are the literal successors of the Poor Knights of Christ and the Temple of Solomon. All I can say is that both bodies have similar philanthropic goals, and both promote Christianity.