The ash is likely to be HIGHLY alkaline...wet ashes are known to be potentially corrosive for that reason. So watch the pH. Plus, grease tends to be fatty acids...so..
The skimmer socks may well save your filter. Skimmer socks are cheap and easy to replace.

I expect you'll need a lot of chlorine to break down the grease, so the more you can physically remove, the better, and it should float on the surface.. Obviously, you cannot use detergents.

While I'm sure it was very traumatic at the time, look at the bright side: You'll have GREAT stories for years!

Carl