Line the existing box from inside
The box is sound, the lid closes, insulation is all that is missing
An insulating lining goes inside the box — moulded polystyrene or rock wool, in the Portuguese retrofit literature; today also thin multilayer panels, made to fit where the shutter still has to roll up. It is the cheapest intervention in the whole opening and it is done from inside, without touching the façade.
Limit: It will not correct a warped lid or a cracked box that lets water in.