Templars, Masons and Mormons, Oh My!!!

"Mormonism" is exactly what it claims to be, a genuine restoration of Primitive Christianity. Mormonism was not at all derived from Freemasonry, but both came from a common source in antiquity. Only Mormonism claims to be a restoration of that source. For a great start in understanding the vast differences and the few commonalities between Mormonism and Freemasonry see Jeff Lindsay's site, Questions About the LDS Temple Ceremony and Masonry. He also has many links to expand one's knowledge on the subject.

Jeffrey M. Bradshaw (LDS), in his article Freemasonry and the Origins of Modern Temple Ordinances, goes through the history in early LDS history of the Freemasons and the Temple Endowment. Be sure to check his references and footnotes as there are a plethora of other excellent articles and books to do a very deep dive into the subject for the serious learner. 

LDS scholar, Eugene Seaich has a very good article at Shields called, WAS FREEMASONRY DERIVED FROM MORMONISM? It goes into ancient history with some very interesting information.

Hugh Nibley (LDS) in Apocryphal Writings and Teachings of the Dead Sea Scrolls tells us that the Masons didn't get their ceremonies they have today from the Apocryphal writings or the teachings of the Dead Sea Scroll documents. Talking about these documents, Nibley explains how:

Nobody had the texts until recently. They do give us an interesting check. The Masonic rites have a lot in common with ours. Of course in part they do have the same source, if you trace them way back. But what a different picture you see. The Masons don't give any religious meaning to them. They think of them as symbolic, as abstract. They don't see any particular realities behind them. The rites have nothing to do with salvation, but consist only of broken fragments. This is obvious if you've seen the Masonic rites and ordinances; they don't hang together. They have been picked up from various times and places, and you can trace them back. Actually, they go back to very early times. These are the ordinances of the Knights Templar and the Hospitalers—two early secret orders imported into Europe at the time of the Crusades. But these were actually based on Solomon's temple and on work for the dead. Read St. Bernard (he wrote both the prologue and the constitution for the Hospitalers, which we have still), who shows that they go back to the time of the Maccabees. At the time of the Maccabees, many of the Jews went off and worshiped false gods; and when they lost the battle, many of the dead were found with pagan amulets around their necks, showing that they had apostatized from the God of Israel. Still they had died as heroes for the cause, and they wondered what they might do to get them saved.
They decided to do their work in the temple by proxy. A vast fund of money was provided to have sacrifices and sin offerings made in the temple in their behalf so that these could be saved in the resurrection.203 This is the tradition carried on by the Knights Templars and Hospitalers—actual work for the dead. But all this was covered up and lost later on.
Lots of people have fragments of these things. The Egyptians had many of them. You can reconstruct from the funerary literature most of the temple ordinances. But you will also find the question, What does this mean? (E.g., in the Book of the Dead 17 and 125.) Some say it means this. Others say it means that. Others say we don't know what it means. It is just a tradition.
So the remnants of these rites and ordinances are found throughout the whole world. But nowhere out there do you find an organic whole in which they fit together and make sense and belong to the plan of salvation. We're the only people that have anything like that."

The modern day Mandaeans of Iraq who trace their religion to John the Baptist have not only secret ordinances but handclasps which are a part of their rites. Handclasps are a fundamental part of many ancient religions and are not just an element of the Freemasons. 

Similarities and Differences
The similarities between the LDS endowment and the Freemason rites are so few compared to the differences; and of those similarities the contexts are different. Only about 5% of the LDS endowment has any similarities with Freemasonry. In contrast, the LDS endowment has a much greater similarity with the ancient mystery teachings taught by Jesus to the apostles after his resurrection. See the links to the 40-day Ministry and the Nag Hammadi texts. Many of the similarities come from the Bible and many can find counter parts from other ancient sources.
None of the signs of LDS temple ceremony can be found in Freemasonry. Only two of the tokens (the first two) of the LDS temple ceremony have any degree of similarity in their forms but are not identical, whereas the other two have no counterpart in Freemasonry.

Mormon critics can produce a list but no context for the list. It is clear that Freemasonry and its traditions played a role in the development of the endowment ritual but not the degree that many of them would like to suggest. They before, they only bring up only similarities not the differences between the two. For example the central story in the endowment is the allegory of Adam and Eve. In Masonry it is the story of the master builder of Solomon's temple Hiram Abiff. Whole vast sections of the Masonic ritual are not and have never been found in the temple endowment.
As one Mormon Mason said:

“The simple fact is that no one ever received their endowment in a Masonic lodge and no one has ever been made a Mason in an LDS temple. As a LDS Freemason I find the similarities reassuring rather than disturbing.”

John A. Tvedtnes' article, Early Christian and Jewish Rituals Related to Temple Practices explains the LDS temple connection to the Jewish temple and the early Christian ordinances and rites.