Suppose that $A$ is a complete neotherian local ring and that we're given a surjective homomorphism
$f: A[[x_{1}, \ldots, x_{n}]] \rightarrow A[[t_{1}, \ldots, t_{m}]]$.
Can we always find a different system of coordinates $y_{i}$ for $A[[x_{1}, \ldots, x_{n}]]$ such that in these new coordinates we have $f(y_{i}) = t_{i}$ for $i \leq m$ and $f(y_{i}) = 0$ for $i > m$?
This is certainly true if $A$ is a field, in which case any lift of $t_{1}, \ldots, t_{m}$ can be completed to a regular sequence by looking at what happens to the tangent space, but I have no intuition outside this case.