Having left the island, went back for a typewriter? (8)

I believe the answer is:

portable

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'for a typewriter?' is the definition.
(portable is a kind of typewriter)

'having left the island went back' is the wordplay.
'having left' becomes 'por' (I can't justify this - if you can you should give a lot more credence to this answer).
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'island' becomes 'elba' (Italian island).
'went back' shows that the letters should be reversed in order.
'elba' reversed gives 'able'.
'por'+'t'+'able'='PORTABLE'

Can you help me to learn more?

(Other definitions for portable that I've seen before include "to take with you" , "Handy - lightweight" , "Able to be carried" , "desirable type of pension" , "easy to bear?" .)

I've seen this clue in the Evening Standard.

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