Answer
Wa `alaykum as-salam wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Marital relationship is something peculiar and should be kept between only the husband and wife.
2- No third party can be involved in this very private relationship.
3- It is not allowed for husband and wife to have intimate relationship in the presence of a third party, and that is why it is not permissible for one of the conjoined twins to get married.
Regarding this issue, the Islamic Research Academy at Al-Azhar issued the following resolution on Thursday, March 27, 2008:
It is not permissible for one of the conjoined twins or both to get married from another person. The reason of prohibition in this case is that marriage has requirements and marital affairs that one of the conjoined twins is not allowed to watch.
It should be noted that the conjoined twins are not considered one person, and it is not permissible for a person to marry from two female conjoined twins as this is considered as combining between two sisters in marriage.
Therefore, the marriage of conjoined twins is contradictory to the rulings of the Islamic Shari`ah in all cases.
Moreover, the eminent Muslim scholar and renowned da`iyah Sheikh `Abdel Khaliq Hasan Ash-Shareef states:
In marriage, spouses display their `awrahs before each other as Almighty Allah permitted husband and wife to have intimate relationship, the thing that is not allowed to be done in the presence of a third party other than the husband and wife. It is clear that the conjoined twins are two persons, and we wonder how what the case would be if one of them married another person.
Therefore, the marriage of one of the conjoined twins to another person is not allowed unless they get separated surgically.
Also, Dr. Rif`at Fawzi, former Professor of Shari`ah at Cairo Univ., adds:
This marriage is not permissible before conducting surgical separation between the conjoined twins. The reason of prohibition is that it is not allowed for a third party (i.e. other than the husband and wife) to see the married couple while having intimate relationship or displaying their `awrahs.
Almighty Allah knows best.