For f = v, see § 145. [...]
Strangely, § 145 doesn't explain how « à cheF » evolved into « acheVer », but §142 (on pp xcii-xciii) claims to do so, but I see no explicit elucidation and so I am still confused.
[...] When v is not final, there is no longer any reason for this strengthening process, and it remains unchanged according to § 140. This is the reason why the feminine of adjectives in -if is -ive; and why we have bovem, bcuf, but bovarius, bout'ier ; navem, nef, but navirium * , navire , servum, serf, but servire, servir; salvum, sauf, but salvare*, sauver; nativum, naif, but nativitatem, naibelé.
The same ruleenables us to explain the relation between the primitive chef and the derivatives chevet, achever, and between such words as brefand brevet, relief and relever.
the same rule explain how à cheF evolved into acheVer?
PS: I don't extract from the more laconic French version; whose entry on 'achever' does not broach the phonological changes.