I was told that if a woman joins the Salaat of a man, then his Salaat becomes invalid while her Salaat is valid.

Answer

In the scenario mentioned by you, it is the opposite. The man's Salaat is valid while the Salaat of the woman is not valid. According to the Hanafi Math-hab, if a woman is in the jamaat, then her Salaat will be valid only if the Imaam makes the intention of being her Imaam. If the Imaam has not made such an intention, then her Salaat will not be valid. It is for this reason that the Salaat of all the women in the Haramain in Makkah and Madinah behind the Imaams is not valid. They do not make intention of leading the women because in their Math-hab there is no need for such an intention.