Good grief. This isn't a stalker, it's a person that he is/was friends with and he made the mistake of trying the 'friends with benefits' thing on and she got hurt.
Those of you that are making her out to be the debbil are off-base, in my opinion.
What he should do depends on his feelings for her. If he wants to maintain a friendship, he should at the very least send a card. If he doesn't, he should stop acting as if he does. Doing so only sets her up for more hurt.
Whether or not the OP's husband cheats has nothing to do with this woman. It has everything to do with him. If the OP believes that he will not cheat, there's no harm in his having female friends. If she thinks that he is a cheater, then she needs to take a closer look at her relationship regardless of whether this other woman is in the picture or not.