Is a man's marriage to his second cousin, immediately after divorcing her first sister (whom he had not consummated the marriage with), permissible or invalid?

Marrying two sisters concurrently is prohibited by Allah's words: (And that you take [in marriage] two sisters concurrently). However, it is permissible to marry the sister [of one's wife] immediately after divorcing her sister with a definitive divorce (ṭalāq bā’in), or after her waiting period (ʿiddah) ends, if she has one. If a man divorces his wife before consummating the marriage or before a valid private seclusion (khalwah ṣaḥīḥah), she has no waiting period and is definitively separated from him. In this case, he may marry her sister immediately, provided the marriage contract with the second sister is concluded with the permission of her guardian (walī) and the presence of witnesses.

However, if he has consummated the marriage with the first wife or had a valid private seclusion with her, and then divorces her with a revocable divorce (ṭalāq rajʿī), then his marriage to the second sister is invalid according to those who consider valid private seclusion to be equivalent to consummation. He must separate from her. If he has already consummated the marriage with his second wife, then sexual intercourse with the first wife is prohibited to him as long as her sister is in her waiting period. It is advisable to consult scholars before proceeding with marriage to avoid leniency regarding marital prohibitions.