I love fried donuts. I think apple, corn, and pumpkin fritters are great. And I don't mind storing used oil properly for another use. It has to be cleaned. And I strain it to get any pieces out.
And I don't reuse leftover animal fat--chicken or fish.
You can strain it through a cheesecloth. But that's messy.
Instead, use a fine strainer, one with a reusable cleanable filter. Strain your oil right back into the jug, seal it, and store it in the refrigerator or dark cupboard.
I'm not going to use my oil over three or four times before discarding it and only then if it is well-filtered.