Choosing $(A,C,F,H,L,S) = (0,5,1,3,1,2)$, we obtain $SCHLAF - FLACHS = 253101 - 110532 = 142569 = 217 \cdot 657$, but $0 = A \neq H = 3$ and $5 = C \neq L = 1$, contradicing the given equivalence.

@above: Sorry, that of course was a typo. It should be $271$ and not $217$ (it appeared correctly in the title and I now also edited the question).

Since $271|10^{5}-1$, the difference is divisible by $271$ if and only if $(10^{4}-10^{2})(C-L)+(10^{3}-10)(H-A)$ is divisible by $271$. Moreover $\text{gcd}(271,990)=1$ and so the last expression is divisible by $271$ iff $10(C-L)+(H-A)$ is divisible by $271$. We have $-271<10(C-L)+(H-A)<271$, because $A,C,H$ and $L$ are digits. Thus this expression is only divisible by $271$ if it equal to $0$. Once again we use that all letters represent digits and so $10(C-L)+(H-A) \Rightarrow C=L \,\text{and}\,H=A$.