In this paper, single-stream transmission in the MIMO interference relay channel is studied. Two independent transceiver pairs with multiple antennas belonging to different operators communicate with the assistance of one relay, which operates in half-duplex mode and employs an amplify-and-forward strategy. The relay that is shared between the two operators also has multiple antennas. First, the interference relay channel is converted to the conventional interference channel via a preliminarily determined relay amplification matrix. Various relay amplification matrices are investigated for this conversion. Then, the flexible coordinated beamforming for the interference relay channel (IRC Flex-CoBF) is proposed for the transceivers. The IRC FlexCoBF algorithm is compared to the alternative schemes proposed in the literature. Simulations show that IRC FlexCoBF achieves a better sum rate performance. Furthermore, a higher robustness to the interferences is demonstrated for IRC FlexCoBF compared to the state of the art. Simulation results show that by sharing a relay between two operators a significant gain in sum rate can be achieved compared to the relay channel.