http://www.seirawanchess.com/articles.html lists a number of endgame puzzles using the elephant and hawk, going over some of the more key checkmate patterns. Always a good place to start if you're wanting to learn more about s-chess.
Something more along the lines of actual tactics puzzles? Not sure. The game's got a small following elsewhere on the web, so try asking about!
I've been waiting for a thread like this because I want to know more about s-chess's opening theory. For instance, are there any openings in regular chess that have proven to be a draw but give a more optimal position in s-chess?
Does anyone know where I can find tactics puzzles using the hawk and elephant pieces used in S-Chess?
I found this wonderful video with Seirawan and Eric Hansen, but otherwise I haven't found anything like this when browsing:
https://www.youtube.com/watch?v=tSXZbbeR-kU&t=2324s