Sketch re-identification (Re-ID) refers to using sketches of pedestrians to retrieve their corresponding photos from surveillance videos. It can track pedestrians according to the sketches drawn based on eyewitnesses without querying pedestrian photos. Although the Sketch Re-ID concept has been proposed, the gap between the sketch and the photo still greatly hinders pedestrian identity matching. Based on the idea of transplantation without rejection, we propose a Cross-Compatible Embedding (CCE) approach to narrow the gap. A Semantic Consistent Feature Construction (SCFC) scheme is simultaneously presented to enhance feature discrimination. Under the guidance of identity consistency, the CCE performs cross modal interchange at the local token level in the Transformer framework, enabling the model to extract modal-compatible features. The SCFC improves the representation ability of features by handling the inconsistency of information in the same location of the sketch and the corresponding pedestrian photo. The SCFC scheme divides the local tokens of pedestrian images with different modes into different groups and assigns specific semantic information to each group for constructing a semantic consistent global feature representation. Experiments on the public Sketch Re-ID dataset confirm the effectiveness of the proposed method and its superiority over existing methods. Experiments on Sketch-based image retrieval datasets QMUL-Shoe-v2 and QMUL-Chair-v2 are conducted to assess the method's generalization. The results show that the proposed method outperforms the state-of-the-art works compared. The source code of our method is available at: https://github.com/lhf12278/CCSC.