Existing proxy re-encryption (PRE) schemes to secure cloud data sharing raise challenges such as supporting the heterogeneous system efficiently and achieving the unbounded feature. To address this problem, we proposed a fast and secure unbounded cross-domain proxy re-encryption scheme, named FABRIC, which enables the delegator to authorize the semi-trusted cloud server to convert one ciphertext of an identity-based encryption (IBE) scheme to another ciphertext of an attribute-based encryption (ABE) scheme. As the first scheme to achieve the feature mentioned above, FABRIC not only enjoys constant computation overhead in the encryption, decryption, and re-encryption phases when the quantity of attributes increases, but is also unbounded such that the new attributes or roles could be adopted into the system anytime. Furthermore, FABRIC achieves adaptive security under the decisional linear assumption (DLIN). Eventually, detailed theoretical and experimental analysis proved that FABRIC enjoys excellent performance in efficiency and practicality in the cloud computing scenario.