We provide a simpler and more efficient way to prove knowledge of the plaintext in (a variant of) the Joye-Libert additively homomorphic cryptosystem. We also extend it into a proof that two ciphertexts encrypt the same plaintext under different public keys. This provides a more efficient instantiation of the Naor-Yung paradigm for IND-CCA2 security than in earlier proofs of plaintext equalities for JL ciphertexts. As a result of independent interest, we show that applying the Naor-Yung technique to similar-looking schemes is non-trivial when the soundness of the NIZK proof of plaintext equality relies on an assumption that directly relates to the infeasibility of recovering the secret key from the public key in the underlying IND-CPA scheme.