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Linear precoding for cooperative multi-cell transmission can provide substantial gains in user throughput, while channel state information (CSI) need to be available at the transmitter. Performance degradation due to imperfect CSI can be partially compensated by robust precoding techniques. For distributed precoding the pre-processing of the user data is performed locally at each base station (BS), while CSI of all participating users is needed. Hence, CSI need to be exchanged between BSs. However, in practice CSI sharing is affected by backhaul latency or limited backhaul capacity resulting in different CSI versions available at the BSs. In this paper, we present a novel robust sum rate maximizing precoding solution, which accounts for imperfect CSI sharing between BSs. Applying the proposed scheme, each BS optimizes its precoding matrix based on local knowledge and by assuming a certain precoding matrix is applied at the other BSs. The assumed precoding matrix results from degrading local knowledge to common but less accurate knowledge. We show that our solution can significantly boost the rate performance compared to existing precoding solutions.