  String backgrounds associated with gauged $G/H$ WZNW models in general depend
non-trivially on $\alpha'$. We note, however, that there exists a local
covariant $\a'$-dependent field redefinition that relates the exact
metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its
leading-order form ($D=2$ black hole). As a consequence, there exists a
`scheme' in which the string effective equations have the latter as an exact
solution. However, the corresponding equation for the tachyon (which, like
other Weyl anomaly coefficients, has scheme-dependent form) still contains
corrections of all orders in $\alpha'$. As a result, the `probes' (the
tachyons) still feel the $\alpha'$-corrected background. The field
redefinitions we discuss contain the dilaton terms in the metric transformation
law. We comment on exact forms of the duality transformation in different
`schemes'.
