As for the contenders of the above letter being a hoax:
 
William Guy Carr
From Wikipedia, the free encyclopedia
 
Confusion has arisen as to the precise source of Carr's Three World Wars scenario. As is the case with many of his claims, Carr does not provide a source for that scenario, but mentions a letter written by Pike and addressed to Italian revolutionary leader 
Giuseppe Mazzini, which outlines a plan for unleashing "Nihilists and Atheists", after World War Three has ended. The confusion was created when Michael Haupt launched his website threeworldwars.com, which mistakenly assumed that Carr also attributed the World War Three scenario to the Pike letter. In fact, the authenticity of this letter is disputed.
[19] Carr states that he learned about the letter from the 
anti-Mason, Cardinal 
Caro y Rodriguez of 
Santiago, 
Chile, author of 
The Mystery of Freemasonry Unveiled (Hawthorne, CA, Christian Book Club of America, 1971). However, Carr's later book, 
Satan, Prince of This World (written in 1959), includes the following footnote: "The Keeper of manuscripts recently informed the author that this letter is NOT catalogued in the 
British Museum Library. It seems strange that a man of Cardinal Rodriguez's knowledge should have said that it WAS in 1925."
[20] More recently, the British Museum confirmed in writing to researcher 
Michael Haupt[21] that such a document has never been in their possession. Pierre-André Taguieff states that Carr gave an ultimate and synthetic account[
clarification needed] of this "legend" that links together the 
Illuminati, Mazzini and Pike in a satanic plot for world domination.
[22]
 
The reference 
Terry Melanson gives a good treatment of the Pike letter, to show the origin of the account of unleashing the nihilists, and that a three world war scenario is not to be found in that material. Michael Haupt had taken the three world war theory from the introduction of Carr's 
Pawns in the Game(1958). This introduction outlines a plan that Carr attributes to Pike, but not to the letter from Pike to Mazzini. Only the last section of the three world war plan in Haupt's text is a quote attributed to the letter from Pike to Mazzini. 
This quote is virtually identical to the one in Rodrique's book and it can be traced to the book Le diable au XIXe siècle (1894) by Gabriel Jagond-Pager aka Leo Taxil, where it is claimed to be from a letter of Pike to Mazzini written in 1871. This quote was later considered to describe the Bolshevik revolution, but whether a hoax or not, it predates 1917. The book of Jagond-Pager is enlisted in the British Museum, which is what Rodrigues meant by his statement, and it contains the full letter be it hoax or not.