Transfer learning has attracted increasing attention in recent years for adaptively borrowing information across different data cohorts in various settings. Cancer registries have been widely used in clinical research because of their easy accessibility and large sample size. Our method is motivated by the question of how to utilize cancer registry data as a complement to improve the estimation precision of individual risks of death for inflammatory breast cancer (IBC) patients at The University of Texas MD Anderson Cancer Center. When transferring information for risk estimation based on the cancer registries (i.e., source cohort) to a single cancer center (i.e., target cohort), time-varying population heterogeneity needs to be appropriately acknowledged. However, there is no literature on how to adaptively transfer knowledge on risk estimation with time-to-event data from the source cohort to the target cohort while adjusting for time-varying differences in event risks between the two sources. Our goal is to address this statistical challenge by developing a transfer learning approach under the Cox proportional hazards model. To allow data-adaptive levels of information borrowing, we impose Lasso penalties on the discrepancies in regression coefficients and baseline hazard functions between the two cohorts, which are jointly solved in the proposed transfer learning algorithm. As shown in the extensive simulation studies, the proposed method yields more precise individualized risk estimation than using the target cohort alone. Meanwhile, our method demonstrates satisfactory robustness against cohort differences compared with the method that directly combines the target and source data in the Cox model. We develop a more accurate risk estimation model for the MD Anderson IBC cohort given various treatment and baseline covariates, while adaptively borrowing information from the National Cancer Database to improve risk assessment.