of unknown origin; attested in London criminal slang as adjective (1775, "counterfeit"), verb (1812, "to rob"), and noun (1851, "a swindle;" of persons 1888, "a swindler"), but probably older. A likely source is feague "to spruce up by artificial means," from German fegen "polish, sweep," also "to clear out, plunder" in colloquial use. "Much of our early thieves' slang is Ger. or Du., and dates from the Thirty Years' War" [Weekley]. Or it may be from Latin facere "to do." Century Dictionary notes that "thieves' slang is shifting and has no history."
The nautical word meaning "one of the windings of a cable or hawser in a coil" probably is unrelated, from Swedish veck "a fold." As a verb, "to feign, simulate" from 1941. To fake it is from 1915, jazz slang; to fake (someone) out is from 1940s, originally in sports. Related: Faked; fakes; faking.
The jazz musician's fake book is attested from 1951. Fake news "journalism that is deliberately misleading" is attested from 1894; popularized in the 2016 U.S. presidential campaign.
-ment
common suffix of Latin origin forming nouns, originally from French and representing Latin -mentum, which was added to verb stems to make nouns indicating the result or product of the action of the verb or the means or instrument of the action. In Vulgar Latin and Old French it came to be used as a formative in nouns of action. French inserts an -e- between the verbal root and the suffix (as in commenc-e-ment from commenc-er; with verbs in ir, -i- is inserted instead (as in sent-i-ment from sentir).
Used with English verb stems from 16c. (for example amazement, betterment, merriment, the last of which also illustrates the habit of turning -y to -i- before this suffix).
The stems to which -ment is normally appended are those of verbs; freaks like oddment & funniment should not be made a precedent of; they are themselves due to misconception of merriment, which is not from the adjective, but from an obsolete verb merry to rejoice. [Fowler]