It's primarily going to depend on what he's specialising in.

If his PhD, and post-doctoral work, will have a more theoretical bent then the (usually) more theoretical "Computer Science"-type courses are probably right.

If he'll be quite practical -- addressing, say, security in real world application development -- then the (usually) very practical "Software Engineering"-type courses are a better bet.

If he's planning on something in a more commercial setting then an "Information Systems"-type degree is probably best bet.

Unfortunately the degree naming/content can vary from institution-to-institution, but in general CS is more theory and SE more coding.

In addition to where he's going, where he's coming from is the other factor. You mention his undergrad's non-technical, but his background will still be a factor -- there are 2 key things his chosen BS needs to do (i) enhance his strenghts, and (ii) fill-in his weaknesses.

Almost certainly what the PhD programmes are after is a demonstration that he's covered all the basics (any IT related course will do this), and demonstration that he's comfortable with highly numerical/logical work (any technical/science degree will do this). in having the masters he's demonstrated he can do academic work at a postgrad level.

Something to consider are the one-year "conversion" masters degrees (usually in IS) -- he should probably check with the departments whether that would be acceptable