Praise be to Allah.
It is not obligatory for the husband to tell the second wife that he is already married and this does not affect the validity of his marriage to her. So long as the marriage contract fulfilled the necessary requirements and conditions, then it is valid.
Shaykh Ibn Jibreen (may Allah preserve him) was asked: Is it essential for the marriage to be valid that a man should inform the woman he wants to marry that he is married to another one, if he is not asked about that? Are there any consequences if he denies it if he is asked?
He replied: The man is not obliged to tell the woman or her family that he is married if they do not ask him, but that cannot usually be hidden because marriage is not usually done except after a period of enquiring and asking about each of the two partners and verifying that they are suitable. But it is not permissible to conceal any facts, and if either party tells a lie and the other party acts on the basis of it, then there is the option of cancelling it. If he says that he is not married and is lying about that, then the woman has the option of annulling the marriage. If they say that she was a virgin when she is not, then he has the option of going ahead with the marriage or cancelling it.