I've had both a 92 and 96, but don't remember if the mags will work in the OTHER frame. I think the guns are almost identical internally. The biggest difference is the opening in the front of the slide and the barrels. (Beretta at one time offered a kit with one frame and both a 9mm and .40 slide, but I don't remember whether they had two sets of mags or one.)
There may be some differences in the mags -- which you might not notice unless you feed hollow-point rounds.
I have an FNS-40 (.40) and also use a 9mm conversion barrel. in that gun. The .40 mags will feed 9mm hardball, but have a real problem with hollow point bullets. The feed lip gap is a bit wider in most .40 mags, and because the 9mm round is also a bit slimmer and the gap is wider, the 9mm round will sit a bit higher as it leaves the magazine -- and the "maw" of some hollow point rounds can bite into the feed ramp and cause a feed stoppage.
I would expect 9mm non-hollow point rounds to work fine in 96 mags, but you might feel a little "clunk" as the round is stripped and fed. Hollow points may be a problem. But unless someone can try it and tell you results, you'll just need have to try it yourself. It won't hurt anything if you do try.