I have used a sifter to screen my ash. It was just a fine screen attached to a few boards. I sifted the ash for about two weeks. The smaller chunks that I recovered burned, but the mess I made for the amount of reclaimed coal that I got, I didn't think was worth it. To each their own.
When I sifted, I did it outside. Still a mess. You can definitely do it, just a matter of if you want to.