Great question!  

(above: skinheads in the UK, circa 1969)

In the late 1950s/early 1960s there was a wave of immigration from Jamaica to England to fill job vacancies there.  The Jamaican immigrants were solidly working-class and tended to settle in working-class neighbourhoods throughout England.

At the time, the English mod subculture was splitting along class lines.  Working-class kids could not keep up with the latest Italian suits and scooters and American R&B records (and amphetamines!) coveted by mods and soon splintered off into their own “hard mod” subculture, which emphasized more working-class style & values.  These hard mods began hanging out with the new kids from Jamaica, who had brought over elements of the Jamaican “rude boy” subculture.

Things took their course and skinhead emerged as a mixture of elements of both the hard mod & rude boy subcultures.  From hard mod came the cropped hair, Doc Martens, donkey jackets, etc.  From rude boy came the short trousers, pork pie hats, and (most importantly!) ska & reggae, etc.

So it was neither “by invitation” nor “cultural appropriation” but rather a natural mixing of the elements of style from two subcultures originating 2700 kms apart from each other that gave us what was possibly the first truly multicultural youth subculture.  

If you’re interested in knowing more about this, we’d recommend having a look at sections of this academic paper as well as Dick Hebdige’s Subculture: The Meaning Of Style.