Can two investigators trade the same spells?
Page 12 on the rules Reference Guide:


  As an action, an investigator can trade any number of possessions with another investigator on his space.  The two investigators may freely give any number of possessions to the other, as long as both investigators agree to this trade.


It's basically telling us that you can trade as many items as you want.  And since each spell is their own piece of cardboard, you can go ahead and trade those back and forth, since there's nothing that says you can't.  Hell, you could trade one clue token for another clue token, since nothing is stopping you.