I am asking on behalf of a relative, a lady of 58 years old; her husband died 10 years ago, in Baghdad when the war was on. She could not bury him in the city where he was born which is about 300km north of Baghdad because of the war. So she buried him in Baghdad. Her husband never left a will and did not tell her to do any thing in case he died, but he always mentioned in conversation that he wished to be back there after death. This lady who is not living in Iraq now, feels that she did not fulfil her husband wishes, and is thinking of digging up the grave and transferring the body to be reburied in the other city.Would you please inform me about the Islamic judgment in this case, whether she should do it or not?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Digging a dead body out of its grave is not permitted, save for dire necessity or a considerable benefit, such as to relocate a corpse of a Muslim that was buried among the graves of non-Muslims, etc. The situation mentioned in your question is not a valid reason to exhume the grave. It causes humiliation to the corpse, may cause his bones to break or his body might disintegrate, so even shifting it is not possible, etc. The location of a grave is not important. One should make Dua' for him and make charities on his behalf. No doubt these acts are more useful and suitable then shifting his corpse without any valid reason in Shariah.
Allah knows best.