There's kind of an accepted idea that after the British spread football around the globe in the last couple of decades of the Victorian period, that foreigners took the game and became better at it than us. The story goes that we'd become so insular and sure of ourselves that being beaten by the Hungarians at Wembley in 1956 was a shock. Some people will tell you that we didn't really learn our lesson and it took us another 40 years, until Arsene Wenger turned up, to actually start taking coaching seriously.
That's kind of true but it's also not. It is true that up until, and after, the First World War, no English club would even consider hiring a professional coach. Mainly because coaching was something that Johnny Foreigner needed, us Brits were innately skilled and intelligent enough to play the game we invented without being told what to do. There were English coaches, such as Steve Bloomer and William Garbutt, taking football abroad though. English coaches were very much in fashion in Austria in the 1920s and they helped to kick-start the so called 'Danubian School' which led to the great Austrian team of the 1930s, featuring Matthias Sinderlar the 'paperman', and eventually to that Hungarian side that beat England at Wembley. Even later on, Vic Buckingham was manager/coach of Ajax between 1959 and 1961 and some people think he helped sow the seeds of what became Rinus Michels' totaal voetbal.
There's a good tradition of English coaches abroad. We just don't hear that much about it.
Garbutt was 1 of 2 English coaches (along with James Richardson Spensley) who ran Genoa C.F.C (Cricket & Football club, which tells you a little something about their origins). Genoa won 9 league titles under those 2 coaches, which is still the 4th highest in Italian Football.
The "father of Argentinian football" was Scottish - Alexander Watson-Hutton. His Alumni team won 10 titles before they were dissolved in 1913. They're joint 6th in the all time titles list with only the 5 "Grandes" being more successful (with an extra 100 years to do it).
Jimmy Hogan managed in Hungary for several years and was at the forefront of creating the foundations that Hungary built the Mighty Magyars on.
I love learning about some of the historical connections in football. We were pioneers and then we gave up the initiative for decades due to what largely seems like arrogance. It's all so incredibly Engish.