Shaykh Salih al-Fawzan explains that a first wife cannot prevent her husband from marrying again nor can she make it a condition to be informed. The key requirement is justice, and the husband must treat all wives equally regardless of whether the first wife knows.
What is the ruling on marrying secretly without the first wife knowing?
She has no connection [authority]. The [first] wife has no authority to prevent her husband [from marrying] or to make it a condition upon him that she is told [about a second marriage]. She should not make such a condition. The important factor [in polygamy] is justice. The husband is obliged to treat [all] his wives equally, whether the first wife knows [about the second] or not.
