I don't like the recycling of oil/fats.  I know that in some deep fyers like the Fry Baby or Fry Daddy, they claim you can leave the oil in the fryer, pop on the cover and use again.
I did that ONCE - and never again - it gave the second days food a funny taste.  And it was for homemade french fries each day - nothing else.
Deep frying fish and then trying to use that oil for something else - YUK!
If I am using shortening in my deep fryer and it is for a two day meal (for fries for Friday fish fry and again for Saturday for Chicken in the basket) then I will do it.  I let the shortening cool, strain through cheesecloth set in a wire mesh strainer and into a non-reactive bowl.  Then I refrigerate it.  
Next day, spoon into the deep fryer to melt and heat.  Once again - cool and instead of straining - I just pour into a bowl - set in the fridge overnight so that it solidifies and then scoop into the trash when it gets hard.
Better safe than sorry.