<p>Transfer learning has gained considerable attention for improving the performance of high-dimensional linear and generalized linear models by leveraging source data. However, few studies have explored transfer learning in multinomial regression (MR) for multi-class classification problems. In this paper, we propose a two-step MR transfer learning estimator when the transferable sources are known and establish its error bounds. When the target and source datasets are close, these bounds can be improved over the MR estimator using only target data under mild conditions. To address the bias introduced by the Lasso penalty, we develop a unified debiasing framework based on KKT conditions, establishing the asymptotic normality for the construction of confidence intervals and hypothesis tests. For practical implementation, a transferable source detection algorithm with theoretical guarantees is proposed. Numerical studies and an application to Genotype-Tissue Expression data demonstrate the effectiveness of our proposed methods.</p>