How to show CPA attacker does not need access to encryption oracle after receiving cyphertext In the private key CPA game, the attacker has access to an encryption oracle anytime during the attack. 

However, I have seen this statement in lecture notes I downloaded "You can prove that for every polynomial time attacker that uses the encryption oracle after receiving the challenge cyphertext, you can construct another polynomial attacker that also breaks the encryption scheme only querying the oracle before receiving the challenge cyphertext."

I have tried to do reductions but I don't see how I could use the first type of attacker to build the second type, since the first requires oracle queries after knowing the challenge cyphertext.

I have also tried to search this but was unable to find.
"You can prove that for every polynomial time attacker that uses the encryption oracle after receiving the challenge cyphertext, you can construct another polynomial attacker that also breaks the encryption scheme only querying the oracle before receiving the challenge cyphertext."


Actually, that is not true in general; you need to make further assumptions on the encryption method.  Presumably, the lecture gave these further assumptions.

One counterexample to the general statement is a self-inverse cipher, that is, one for which $E_k(E_k(M)) = M$.  It is obvious, given $E_k(M)$ and an encryption oracle, how to recover $M$ with a single query.  However, if there are no further weaknesses, there is no useful way to generate queries before you see the challenge ciphertext $E_k(M)$.