An interesting summary from Hrach Martirosyan about the phoneme [f] in Armenian.
PIE didn't have *f. So all occurrences in daughter languages are the result of later development.
In Armenian the phonetic shift p>h occured with an intermediate stage p>f>h. An indirect evidence that the Bronze Age Armenian had *f is the Kartvelian word phoni , a loanword from Armenia *fon later known as hun (հուն river/stream bed). This word stems from PIE *pont-. The Greek pontos meaning sea is also from the same root.
In fifth century when Mashtots was inventing the alphabet Armenian didn't have an [f]. Various letters p', w, or h (փ, ւ, հ ) were used in loanwords from Iranian and Greek were f was present.
In Middle Ages the new letter f ( Ֆ/ֆ) was introduced in Armenian alphabet.