Authenticity of the Pontius Pilate's letter to Tiberius Caesar? Just looking to find out if this alleged Letter of Pontius Pilate to Tiberius Caesar is authentic or a later forgery? I don't care how it physically describes Jesus, just want to know how it was found and why it's claimed authentic or not. Thanks.
I would say probable forgery. First searching for the letter before a link/source was added revealed at least 3 letters, each is written differently:


Letter of Pilate to Tiberius 1 - Unable to verify by finding an image of the original Greek manuscript
Letter from Pontius Pilate to Tiberius Caesar - mentions Copies are in the Congressional Library in Washington, D.C. but initial searches reveal nothing, and some sites say mention:


  "The Library of Congress has received a number of inquiries over the years about a purported letter from Pontius Pilate to Tiberius Caesar concerning Jesus Christ. The Library does not have such a letter in its collections".

Fraud by Pilate Letter - although this seems to be claiming the letter is false (I google translated it), the text of this letter is unique from the other two. This also mentions a fiction book, Letters of Pontius Pilate, published in 1928 which may be the basis for many of the supposed letters that mention Jesus
Historic Letter written by Pontius Pilate to Tiberius Caesar - mentioned in OP question mentions it is in the British Museum but searches on that site and of the British Museum Library reveal nothing


I've found a supposed response from the British Museum


  There are no surviving original letters by Herod or Pontius Pilate, to each other or to anyone else. Any manuscripts of them which do exist are forgeries or much later copies. A Syriac MS in the British Library Oriental Collections (reference number Add. 14609) contains a 6th or 7th Century copy of the letters. Here is the catalogue description of the MS:
  
  THE DOCTRINE Of St. Peter;-The life of St. Anthony, by St. Athan- 
  asius;-Account of the Monks in Egypt;-Life of Serapion;- 
  Letter of Herod to Pilate, and of Pilate to Herod;-The Recogni- 
  tions of St. Clement. On vellum, of the vith or viith century. 
  Quarto. [14,609.]
  
  There are many modern texts and English translations of the letters, including the one on the website link you gave. 
  
  I hope this helps.
  
  Yours sincerely,
  
  Zoë Stansell 2
  
  MSS Enquiries


In favor of the a letter from Pilate concerning Jesus is this book, Archaeological Writings of the Sanhedrin and Talmuds of the Jews by William Dennes Mahan, page 205. This and other sources might be considered pseudipigrapha and Apocrypha. 

One to thing to remember is that Pontius Pilate was a Roman prefect for the province of Judaea under Empereor Tiberius Caesar. There probably was correspondences, reports, and/or letters between them.

To answer the second question there is an article talking about when one letter was discovered in Liverpool in 1964 and goes into detail on why he believes it to be a fraud. 

Emphasis added by me

1 source is Ante-Nicene Fathers page 459, which is also in English

2 She appears to actually work at the British Library, see the author