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Icons can only be crisp if they are drawn from start to finish “crisp”. Trying to edit an already made icon that isn’t “crisp” will prove difficult if you’re not familiar with pixel-perfect drawing. Pixel-perfect is exactly like it sounds. It’s color/shape is dead to the pixel, no fallout color. (Or whatever the proper terminology is!) This is the best way to achieve crispy icons, creating “pixel-perfect” drawings. Search for it. It’s basically like using the pencil tool in Photoshop instead of the brush tool. Even if Hardness is 100% on a brush in Photoshop, doesn’t mean it’s dead to the 1px brush you’ve set, whereas the Pencil tool will be.
If your friend made it in illustrator, he should send you a larger version than 22×22, considering illustrator is vector-based, it can be scaled to absolutely any size. Then in return, you scale it down in “Constrained” proportions and it should be crisp.
I zoomed right in to that icon you’re talking about and the pixel color spread is everywhere. Had you edited this before you uploaded it?