One way to do this mechanically, is to rely on a fix at the back of the window board, using a bare face tenon along the length of the window board, inserted into the groove on the inside of the window sill.
The front is fastened down using Galvanised strap or angle brackets screwed to the underneath of the board, and to the wall beneath This is more convenient to do before plastering, but it is a simple enough operation to house the straps deep enough into the plaster and fill after fixing.
EDIT.
For a really neat fix, the sides of the window board can be partly recessed into the reveals, cutting the tops and bottoms of the housing with a multitool, before chiselling out the waste, and filling after the board has been installed.