The term of “convert” (new believer) refers to person who have just converted to Islam. In the ownership of property, Muslim or non-Muslim, regardless new believer or not, have their full rights to own any assets. As well as in transferring wealth during their lifetime, Islamic law also permits Muslim or non-Muslim to pass the property among them without any restraint or limit, such as by selling or purchasing, leasing, gift, endowment or will. 

However in cases after death, there are provisions that property of a Muslim cannot be transmitted to his non-Muslim parents or sons. Except under join-ownership, wills or maintenance, Muslim and non-Muslim have different rights as a spouse, kids or dependants as their personal rights. Thus, non-Muslim will not inherit from Muslim although both of them shared the same blood-tie. Hence, in the case of new believer, indirectly, their adherence to Islam has deprived both sides from inheritance. As for Islam, the differences of religion limit the process of transmitting wealth and at the same time, their relationship and responsibility as one family still be acknowledged and enforced among them.