Kyber, a key encapsulation mechanism based on lattice problems, was the first to be standardized by the National Institute of Standards and Technology (NIST) in 2023. Kyber-AKE, a weak forward-secure authenticated key exchange (AKE) protocol, was constructed by the designers of Kyber and derives session keys in two rounds using three IND-CCA secure key encapsulation mechanisms. This study introduces Kyber-PFS-AKE, a newly proposed authenticated key exchange protocol. In Kyber-PFS-AKE, only IND-CPA secure public-key encryption is utilized, and decryption errors within IND-CPA secure encryption are addressed using the re-encryption technique within the FO transformation, thus simplifying the design of post-quantum Kyber-AKE. A rigorous proof demonstrates that certain operations in the Kyber-AKE protocol are redundant. By eliminating these redundancies, the protocol achieves a simpler and more efficient design. The session key indistinguishability and perfect forward security of Kyber-PFS-AKE are formally proven within the eCK-PFS-PSK model. The proposed Kyber-PFS-AKE is implemented using Kyber-768. PKE with 165-bit quantum security. Experimental results show that compared to Kyber-AKE, the computation time for the initiator is reduced by 38%, while the computation time for the responder is reduced by 30%.