Question: Who invented the cipher machine of which Typex was an adaptation ? 

Context paragraphs:
Beaufort cipher: The Beaufort cipher, created by Sir Francis Beaufort, is a substitution cipher similar to the Vigenère cipher, with a slightly modified enciphering mechanism and tableau.  Its most famous application was in a rotor-based cipher machine, the Hagelin M-209.  The Beaufort cipher is based on the Beaufort square which is essentially the same as a Vigenère square but in reverse order starting with the letter "Z" in the first row, where the first row and the last column serve the same purpose.

Typex: In the history of cryptography, Typex (alternatively, Type X or TypeX) machines were British cipher machines used from 1937.  It was an adaptation of the commercial German Enigma with a number of enhancements that greatly increased its security.  The cipher machine (and its many revisions) was used until the mid-1950s when other more modern military encryption systems came into use.

Heath Robinson (codebreaking machine): Heath Robinson was a machine used by British codebreakers at the Government Code and Cypher School (GC&CS) at Bletchley Park during World War II in Cryptanalysis of the Lorenz cipher.  This achieved the decryption of messages in the German teleprinter cipher produced by the Lorenz SZ40/42 in-line cipher machine.  Both the cipher and the machines were called "Tunny" by the codebreakers, who named different German teleprinter ciphers after fish.  It was mainly an electro-mechanical machine, containing no more than a couple of dozen valves (vacuum tubes), and was the predecessor to the electronic Colossus computer.  It was dubbed "Heath Robinson" by the Wrens who operated it, after cartoonist William Heath Robinson, who drew immensely complicated mechanical devices for simple tasks, similar to (and somewhat predating) Rube Goldberg in the USA.

M-209: In cryptography, the M-209, designated CSP-1500 by the United States Navy (C-38 by the manufacturer) is a portable, mechanical cipher machine used by the US military primarily in World War II, though it remained in active use through the Korean War.  The M-209 was designed by Swedish cryptographer Boris Hagelin in response to a request for such a portable cipher machine, and was an improvement of an earlier machine, the C-36.

Enigma machine: The Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial, diplomatic and military communication.  Enigma was invented by the German engineer Arthur Scherbius at the end of World War I.  Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II.  Several different Enigma models were produced, but the German military models, having a plugboard, were the most complex.  Japanese and Italian models were also in use.

BID 610: BID 610 or Alvis was a British cipher machine used by both British and Canadian governments.  It was the first fully transistorised full-duplex online cipher machine used by the British Army.  It was introduced in the 1960s.

Grill (cryptology): The grill method (Polish: "metoda rusztu" ), in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau ("Biuro Szyfrów") in decrypting German Enigma machine ciphers.  The Enigma rotor cipher machine changes plaintext characters into cipher text using a different permutation for each character, and so implements a polyalphabetic substitution cipher.

JADE (cypher machine): JADE was the codename given by US codebreakers to a Japanese World War II cipher machine.  The Imperial Japanese Navy used the machine for communications from late 1942 until 1944.  JADE was similar to another cipher machine, CORAL, with the main difference that JADE was used to encipher messages in katakana using an alphabet of 50 symbols.

Combined Cipher Machine: The Combined Cipher Machine (CCM) (or Combined Cypher Machine) was a common cipher machine system for securing Allied communications during World War II and for a few years after amongst NATO.  The British Typex machine and the US ECM Mark II were both modified so that they were interoperable.

Mercury (cipher machine): Mercury was a British cipher machine used by the Air Ministry from 1950 until at least the early 1960s.  Mercury was an online rotor machine descended from Typex, but modified to achieve a longer cycle length using a so-called "double-drum basket" system.

Supporting paragraphs: Typex Enigma machine
Answer: Arthur Scherbius