As shown in the Wiktionary:
From Proto-Indo-European *sriges-, *sriHges-.
But I can't find the clue to this sound change on Wikipedia, which concludes that PIE*bʰ, *dʰ, *gʷʰ will become L. f-, when they are "At the beginning of a word".
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I don't think we ever know for sure how a sound change happens. We can deduce what changes have happened (and sometimes experience what changes are happening), and we can certainly conjecture about the phonetic processes involved, but we can never really answer how (or why) questions.
Here, the obvious conjecture is that in that context, the fricative /s/ came to be replaced by a different fricative /f/. In other places the sequence became /ʃr/ or /str/, suggesting that it is often found to be awkward. I also notice that when I pronounce /sr/ I have a tendency to project my lower lip. If I happen to protrude my upper lip a bit, it can become /sfr/ (actually /sφr/, with a bilabial fricative).
Notice that the other examples you give are difficult to understand unless you assume that they went through a fricative stage such as /β/, /ð/ or /ɣ/; then the probable process would again be substitution of the different fricative /f/.
You can see a similar process at work currently in dialects of English where /θ/ (as in think) appears as /f/.