Is it permissible for the husband to marry a second wife despite the refusal of his first wife, who does not menstruate, and without the husband's knowledge?

Polygyny is something that Allah has legislated if the one desiring it is capable of fulfilling the rights that stem from it. It is not affected by whether the first wife menstruates or not, nor by whether the husband is aware of this or not. It is permissible for the husband to marry a second wife even if his first wife refuses, provided he meets the conditions that permit polygyny, whether his first wife menstruates or not.