Here's the example that caused the question
$$ y(t) = x_1(t-3) \circledast x_2(-t+2) \quad x_1(t) = e^{-4t}u(t) \quad x_2(t) = e^{-2t}u(t)$$
For $x_1$, the $t-3$ factor can be adjusted to be (time shifting) $$ e^{-3s} \mathcal{L}\{ x_1(t)\} $$
but, for $x_2$, can the $-t+2$ be changed to $$ e^{2s} \mathcal{L}\{ x_2(t)\} $$