You're reversing cause and effect. Trump latched onto the term after the entire press started blaming his victory on "fake news" - that's where he got the idea from. (A lot of his ideas seem to just be whatever's been in the press last, actually.)
I am aware that Trump got the idea from the press, my point was that had Trump not stolen the term as a coverall for news stories he disagrees with then term would have been largely forgotten.
The Google trends map in the comment I replied to shows the original peak in Novermber of 2016 which I think started when Buzzfeed ran an article about fake news stories having more engagement on Facebook than true news stories leading up to the election. [1]
There's another peak in early December that is probably from Hillary mentioning it in a speech. [2]
There's a third peak in January which is probably from when Trump wouldn't let Jim Acosta ask a question and called him and CNN fake news. [3]
After that, it was officially added into Trumpian vernacular. Had he not started using the term incorrectly on a regular basis, we would not have seen the continued popularity of the word that the graph shows after December 2016. There would have been some peaks due to various academic studies about actual fake news coming out and being reported on but most of the popularity and staying power comes from Trump.
