Is it permissible to give as charity money obtained from forgery during overtime hours, and is it permissible for a Muslim to take this money from its owner to give it as charity?

Your friend has done well by willingly seeking to absolve himself of the public funds he wrongfully took, because its sanctity is great and its sin is grave. The Prophet, peace and blessings be upon him, warned against taking it without right. The way to dispose of ill-gotten wealth is to return it to the entity from which it was taken. If that is not possible, it should be spent on the general welfare of the Muslims or given to the poor and needy. He may handle the matter himself or delegate someone else to do so on his behalf.