The following is the response of the maraji' to your inquiry:
It is haram to exhume the body of a dead believer. But in some cases, it will be permissible, namely:
1. When the dead body has been buried in a usurped land and the owner of the land is not willing to let it remain there.
2. When the shroud of the dead body or any other thing buried with it has been usurped and the owner of the thing in question is not willing to let it remain in the grave. Similarly, if anything belonging to the heirs has been buried along with the deceased and the heirs are not willing to let it remain in the grave. 3. When it transpires that the deceased was buried without Ghusl or Kafan, or the Ghusl was void, or he was not given Kafan according to religious rules, or was not laid in the grave facing the Qibla.
4. When it is necessary to inspect the body of the dead person to establish a right which is more important than exhumation.
5. When the dead body of a Muslim has been buried at a place which is against sanctity, like, when it has been buried in the graveyard of non-Muslim or at a place of garbage.
6. When the grave is opened up for a legal purpose which is more important than exhumation. For example, when it is proposed to take out a living child from the womb of a buried woman.
7. When it is feared that a wild beast would tear up the corpse or it will be carried away by flood or exhumed by the enemy.
8. In the case of there being the intention of burying a part of the body of the deceased that wasn't buried with it, but as per obligatory precaution, it must be set in the grave in a way that the body is not seen.
9. To transfer the body to one of the sacred places, provided that doing so does not result in any disrespect to the deceased.
In addition to the above, sometimes because of certain significant reasons (such as urbanization), a grave needs to be relocated, and this is done with the permission of the religious authority.
 Tawdih al-Masaa'il (annotated by Imam Khomeini), vol. 1, pg. 349.
 Grand Ayatullahs: Khu'i, Tabrizi, Zanjani, Fazel, Sistani, Saafi, Bahjat; Ibid, pg. 351.