Physical Unclonable Functions (PUFs) are widely used in hardware security due to their inherent unclonability and randomness. However, the temporal instability of strong PUFs remains a barrier to their adoption in latest PUF-based cryptographic protocols, as it incurs significant overhead from error correction. In this paper, we propose PS-PUF, a novel architecture that leverages weak PUFs and cryptographically secure pseudorandom functions (PRFs) to construct a pseudo-strong PUF with stable and reproducible outputs. Our design includes a PRF for secure mapping, and a buffer to optimize performance in batch-access scenarios. We formally analyze the threat surface of PS-PUF and provide cryptographic security proofs showing resistance against modeling attacks. Implemented on the Genesys 2 FPGA, PS-PUF achieves at least 2.72× in batch scenarios with negligible hardware overhead and a maximum performance reduction of 10.7%, enabled by reusing the PRF module in integrated environments.