First, project manager can mean a lot of different things. Some of those she probably is qualified for, but most she is not. Business Analyst is a different. At the risk of offending some business analysts here, I do not think the job requires much in the way of hard technical skills. Is your wife a good, active listener. Does she communicate well with people, even difficult people. Is she someone who notices problems where others do not? Can she talk to both a gregarious department manager, an irresponsible hourly wage earner answering phones, and a socially awkward developer? Can she talk to people of different ethnic backgrounds and understand them and not get frustrated?
Depending on the exact role, she will probably need basic MS Office skills and maybe some SQL knowledge. BA's often end up acting as a QA as well, so she should look into some of the lingo and jargon in the QA field. Going from admin to BA is not a big jump, and if she can get past the HR screening process, she can do the job.