Wearing wig is allowed in Islam, but if a woman wears it, she must cover it as a part of her Hijab obligation. Some Jewish women wear wig and consider it a full cover of the hair but in Islam wearing wig does not mean any change in Hijab obligation.

Those who need to wear wigs should not hide it when they propose or are been proposed for marriage as marriage must be built on true facts about both with out hiding such things.

Wassalam