Not easily. The '65 headlight ***emblies (and fender housing) are wider than the '63 parking light /turn signals of the '63.
An easier solution is to make/buy a custom grill or get a 65 grill and just mount your headlights behind the turn signal grilles.
Note to WATKINS BOYZ: The '65 headlight mounting ***embly will still be too wide for this type of installation. (I tried it on my '64.)
Yeah, but if you use the '63-4 fender grilles you can put any old headlight ***embly in there. So to use '65 hidden lights on a 63-4 you need to use '65 fenders then? Honestly I think that using some other light behind the original fender piece is going to be the best bet, unless you can buy a parts car cheap or get lucky at the pick-n-pull those '65 light units are big damned $$$$ to buy. In fact, the right options on a Riviera and I would buy a $500 one any day to part out.
Why not just build a custom grille that covers the headlights in their current location? Same look (at least during the day) and a lot less work.