= Solution
Let $D$ be <simply connected domain> with distinct marked boundary points $a,b$, and choose a <conformal map> $f:D\to\mathbb H$ with $f(a)=0$ and $f(b)=\infty$. Chordal $\operatorname{SLE}_\kappa$ from $a$ to $b$ is the unparameterized curve $f^{-1}(\gamma)$, where $\gamma$ is chordal SLE in $(\mathbb H,0,\infty)$.
Any other such map is $\widetilde f=rf$ for some $r>0$. The <Scaling invariance of SLE> says that $r^{-1}\gamma$ has the same unparameterized law as $\gamma$; only its capacity clock changes. Hence the pullback law is independent of $f$. This proves the <Conformal invariance of SLE> definition is well-defined.
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