Is it permissible for a married woman to speak with her friend who was previously forbidden from speaking with her due to her relationship with her friend's brother?

There is no harm in speaking with your friend, as long as it does not lead to any corruption, and provided that it is limited to conversation without visits. It is preferable that this be with the knowledge of your family, for fear of damaging your reputation, or causing ill-will, or the news reaching your husband.