Encrypting AES cipher text with fully homomorphic encryption Suppose I run a fully homomorphic encryption scheme (FHE) on a cipher text c, generated by running AES on plain text m and get c' as the output.

What would the output be if decryption of AES is run on c'? Would the decryption of c' using AES key result in a cipher text that decrypts to m if the decryption function of the FHE was applied?
No, this won't happen. You can't change the order of operations. For that to happen, you'd have to homomorphically compute the decryption function of AES on the encrypted ciphertext c'.