Asymmetry in converting Burrows-Wheeler transform to suffix array?
It's possible to build the suffix array of $s$ in linear time from $s$ and $BWT(s)$ in a somewhat easy way. You do need to build a rank-select data structure on $s$ in order to do this.

To see how to do this, look at Ferragina and Manzini's paper "The FM-Index". The LF mapping they describe also essentially computes the suffix array.