Is it permissible to store a man's sperm, and is it permissible for his wife to use it for artificial insemination after his death?

Insemination with the husband's sperm after his death is prohibited, whether during the 'iddah (waiting period) or after it; because the marital bond is severed by death. As for the permissibility of washing the deceased, it is not proof of the continuation of the marital bond.