It should as HD sells a Fat Bob/Wide Glide style fender for conversion of the other Dynas.
The FB/WG fender requires a different installation kit which has to be purchased separately. You would have to reverse this and buy the parts separately to make the fender fit. A good parts guy could help you and be sure you get the Accessories and Parts catalog.
The Fat Bob has a 180/70 16 tire which is wider than the Superglide's 160 but it should still fit OK. HD also sells a 180 tire and installation conversion for the Dynas. The seat should also fit with just a change in position of the seat-to-fender mounting nut.
Bring money if you go that route, or find someone who wants to swap fenders and has the matching color. Think it through before you act, however, as the rear fender is part of the charm.