The recent expansion of the Internet of things (IoT) and its applications continues to dramatically change the IT services supporting manufacturing, energy management, intelligent transportation, smart cities, etc. These IT services often interconnect Internet-based Cloud systems with IoT or intelligent smart devices held by organisations. As IoT devices are resource-limited, the security of their communication is provided by lightweight cryptography that could consequently lead to the devices being insecure against a quantum adversary. On the other hand, Internet Cloud systems are resource-rich and could easily support post-quantum cryptography. This paper presents a proxy re-encryption scheme that translates ciphertexts of a classical lightweight encryption algorithm into their post quantum equivalent and vice versa. More precisely, we propose a lattice-based ABE-IBE (L ABE-IBE) proxy re-encryption scheme that transforms a classical lightweight ciphertext into a lattice based ciphertext. We compare our proposed L ABE-IBE proxy re-encryption scheme with classical proxy re-encryption (ABEIBE) schemes. We discuss the security and efficiency of our construction.