Is it permissible for the husband to register the house and car in the wife's name from their joint property?

The basic principle is that the husband is responsible for the financial support of the household, his wife, and children. A wife's assistance to her husband in spending is good and rewarded. It is permissible to mix the spouses' money and spend from it without distinction. If they wish to purchase a house or a car and each consents, there is no objection, and what is purchased will be equally owned by them. Each of them may gift their share to the other, and the donee takes possession of the gift upon its receipt and acquisition. This is supported by the hadith of the Ash'aris regarding the mixing of their provisions and dividing them equally, which shows the permissibility of gifting an unknown item and the virtue of altruism and equality.