Yes, the fear should and can be overcome, for safety, satisfaction and fun.
Sign her up with a patient instructor who teaches a small class - perhaps at community college - and who specializes in adult non-swimmers. Encourage her to attend often and regularly, and not be discouraged.
An alternative would be individual instruction, but she may find the encouragement and comradery of a group to be most helpful and supportive. Others have.
Last edited by borate : 06-04-2016 at 11:38 PM.