Wavelet Filter Coefficients from Scaling Filter Coefficients
For perfect reconstruction you need:

$$ g \left[ n \right] * \hat{g} \left[ n \right] + h \left[ n \right] * \hat{h} \left[ n \right] = \delta \left[ n \right] $$

Where $ g \left[ n \right] $ is the Analysis Wavelet Function, $ \hat{g} \left[ n \right] $ is the Synthesis Wavelet Function, $ h \left[ n \right] $ Analysis Scaling Function and $ \hat{h} \left[ n \right] $ is the Synthesis Scaling Function.

Practically, Scaling Function is the LPF and Wavelet Function is the HPF.