So I am little wodering how an automatic "one button" transfer could word like this? Is there an "easy" way ?

Yeah, by definition a minimum phase system is one where the phase can be derived from the negative of the Hilbert transform of the log-magnitude response.

One way to compute the MPT is the following:

The complex cepstrum of a minimum phase signal is causal - i.e. 0 for negative time.

You can derive the complex cepstrum from the real cepstrum, given their relationship: i.e.

Rceps(n) = (Cceps(n) + Cceps(-n))/2; // i.e. the even part of the complex spectrum

CCeps(n) = 0, for n < 0; //i.e causal for minimum phase

CCeps(0) = Rceps(0);

CCeps(n) = 2*Rceps(n);

To estimate the real cepstrum you can do IFFT(ln(abs(FFT(original_ir))))

The forward transform of that complex cepstrum would then give you the minimum phase version of the original IR.

To forward transform the estimate of the complex cepstrum: IFFT(e^(FFT(CCeps)));

Just be aware of aliasing, since we are estimating the complex cepstrum with a DFT (in other words use a big enough FFT size)