I would have replaced the board (it seems to have served its purpose), added insulation (perhaps 50mm polystyrene, or whatever fits), and then another board on the inside.
On the outside, I would have used facade sealant (or similar - but NOT silicone) around the edges to ensure it's properly sealed, both to prevent water/meltwater from seeping in at the bottom over time and to seal against drafts, and then painted it.
That way, you should have a solution that works over time, warmer and reduced cold drafts, and less risk of condensation on the inside.
A quick solution, if you can't do the whole job now in the winter, is a polystyrene board that you press on the inside for the time being as mentioned above, and then you can do the renovation when the weather is warmer. It won't remove the mold, but it will provide some insulation against potential spores for a short time anyway. But I believe it needs to be addressed because otherwise, there's also a risk that moisture damage will spread to the window sill/facade over time...