Turn acausal Butterworth output into output of a causal Butterworth without input signal
This is possible, as long as you know the filter which was applied to the data in the first place.

Assuming that the original acausal filter is $H_a(\omega)$ and your filtered data is $Y_a(\omega)$, then the original data $X(\omega)$ can be retrieved by inversely applying the filter to the data:
\begin{equation}
X(\omega) = \frac{Y_a(\omega)}{H_a(\omega)}
\end{equation}

This is simply a re-arrangement of the equation which can be used to describe the initial  filtering operation:
\begin{equation}
Y_a(\omega) = X(\omega) H_a(\omega)
\end{equation}

I've illustrated the concept using frequency domain notation, but the concept is the same for the time domain.  Depending upon your acausal filter, you may encounter some problems inverting it, I don't think this will be an issue in this case.