Previously plywood, as a core material in the transom, was popular. The problems of water penetration and rotting the plywood has been discovered over the past few years so if possible try and avoid any plywood except in the interior fitting out of your fiberglass boat.
If you are building a powerboat and planning an outboard or stern drive installation, then the plywood cored transom is a possibility but make sure the plywood is of the best quality marine grade. As your transom will have some camber or curve, you can pre-laminate several layers of thin plywood to this camber and after cutting to the approximate shape install in position, on the mould. Now you can trim the transom to the exact shape to allow it to tie in with the side of the hull. Make sure you fasten the transom from inside the mould so you can release it after turnover and before you remove the mould from the hull.
You may prefer to laminate the plywood transom in place. In this case, install the first layer by screwing from inside the mould and then laminating the other layers of plywood on to the first, by gluing and stapling from the outside. You should fit the transom so that the plywood overlaps the core on the hull and then radius the outer edges. All edges on the hull must have a radius before the first layer of fibreglass
