Break AES-CFB mode having access to a AES-CTR black box I need help for a "simple" problem

Let's suppose an intercepted ciphertext C encrypted with an AES-CFB mode of operation, using key K and some IV (IV is probably at the begining of C)

The system let us access to a black box encrypting any tupple (plaintext, IV) using AES-CTR mode with the same key K. 

I succeed compute the keystream of the CTR mode using output of the black box, but I still need the keystream of the CFB mode before decrypting C. 

Anyone has an idea how to do it ? 
Thanks
It is quite easy, try to imagine if you have only one block of plaintext and you encrypt it under CFB or CTR with the same IV... 
(using the black box you can actually get the encryption of any IV of your choice)