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I know it's unnecessary to change filters, but would it be detrimental to my fish if I gave my filter to my friend to help him cycle his tank? Or is that not even helpful to his tank?
You need your filter to maintain your cycle. The best way would be have your friend run his filter on your tank, with your filter running for a couple of weeks.
I am assuming you mean the whole filter not the media.
You could give him half of yours do not take all of your media out. You could also give him some of your gravel If it does not match he could hang it in a bag.