We report a simple and compact implementation for single-pass second-harmonic-generation (SP-SHG) of cw laser radiation, based on a cascaded multicrystal (MC) scheme, that can provide the highest conversion efficiency at any given fundamental power. By deploying a suitable number of identical 30-mm-long MgO:sPPLT crystals in a cascade and a $30\mathrm{W}$ cw Yb-fiber laser at $1064\mathrm{nm}$ as the fundamental source, we demonstrate SP-SHG into the green with a conversion efficiency as high as 56% in the low-power as well as the high-power regime, providing $5.6\mathrm{W}$ of green output for $10\mathrm{W}$ and $13\mathrm{W}$ of green output for $25.1\mathrm{W}$ of input pump power. The MC scheme permits substantial increase in cw SP-SHG efficiency compared to the conventional single-crystal scheme without compromising performance with regard to power stability and beam quality.