Entanglement distribution between distant parties is one of the most important and challenging tasks in quantum communication. Distribution of photonic entangled states using optical fiber links is a fundamental building block toward quantum networks. Among the different degrees of freedom, orbital angular momentum (OAM) is one of the most promising due to its natural capability to encode high dimensional quantum states. We experimentally demonstrate fiber distribution of hybrid polarization-vector vortex entangled photon pairs. To this end, we exploit a recently developed air-core fiber that supports OAM modes. High fidelity distribution of the entangled states is demonstrated by performing quantum state tomography in the polarization-OAM Hilbert space after fiber propagation and by violations of Bell inequalities and multipartite entanglement tests. The results open new scenarios for quantum applications where correlated complex states can be transmitted by exploiting the vectorial nature of light.