iPhone 5 verizon nano sim

I had my verizon iphone 5 stolen. i still have the nano sim because it was not in it at the time. a friend has offered me an unlocked at&t iphone 4s. i understand that the sim cards for the two are different sizes but i have an adapter to overcome that.

my question is: will the verizon nano sim be compatible with the unlocked at&t 4s? i have heard contradicting things and am not sure what to believe