Is a lawful marriage to a man who is already married to two women, with an apartment written in the new wife's name in her country, without a marriage permit, impermissible or permissible?

A husband must be just among his wives regarding maintenance, lodging, housing, and clothing. This obligation does not cease even if they are in distant places, unless the wife relinquishes her right. It is permissible for a husband to register an apartment in his wife’s name as part of her mahr (dowry), and he is not obligated to give his other wives the like, because justice is not required in the mahr. The wife is advised to document her marriage contract to preserve her rights and the rights of her children.