(S)-1-bromo-1-fluoroethane reacts with sodium methoxide to give pure (S)-1-fluoro-1-methoxyethane.
This is an SN2 reaction so inversion should take place , hence the product should be R but it is not so . Why?
You're right in that the SN2 Reaction Mechanism will invert the stereocenter. However, the naming convention is based on relative priority and the mechanism by which the product is formed has little to do in how it is named. This appears to be where your confusion lies since you're associating the mechanism and the named configuration when they are not related at all
In the case of an SN2 reaction:
If the attacking nucleophile had the same relative priority as the leaving group (in this case anything with an atomic number > F, since Br is the heaviest among H, F, and C), then you're right, S would turn into R.
However, in the case you quote the nucleophile is MeO-, and O has an atomic number lower than F. Following the CIP rules, we would have to assign the absolute configuration of 'S' even though the stereocenter has been inverted relative to the original compound.