All the letters of Plath Bea devoured (8)

I believe the answer is:

alphabet

I'm a little stuck... Click here to teach me more about this clue!

'all the letters' is the definition.

'plath bea devoured' is the wordplay.
'plath bea' anagrams to 'ALPHABET'.
Though, I'm unsure how this is indicated.

'of' is the link.

Can you help me to learn more?

(Other definitions for alphabet that I've seen before include "A to Z inclusive" , "Confusing assortment of initials" , "First elements (of language)" , "Letters, symbols used in a writing system" , "lots of characters" .)

I've seen this clue in The Sun and The Times.

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