That vowels and consonants can be allophones of the same phoneme (such as a vowel-like approximant being an allophone of a consonant phoneme, e.g., /w/ or /j/ alternating with vowels, or syllabic consonants) is a matter of basic linguistic definition and common knowledge.
The claim refers to a standard linguistic phenomenon where sounds traditionally classed as vowels and consonants can function as allophones of a single phoneme (for example, glides like [j] and [w] alternating with high vowels [i] and [u] in phonological rules across various languages). This is a textbook definition in phonology and constitutes common knowledge, requiring no specific retrieved paper for verification.