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Deep learning techniques are dominating automated animal activity recognition (AAR) tasks with wearable sensors due to their high performance on large-scale labelled data. However, current deep learning-based AAR models are trained solely on datasets of individual animal species, constraining their applicability in practice and performing poorly when training data are limited. In this study, we propose a one-for-many framework, dubbed Cross-species Knowledge Sharing and Preserving (CKSP), based on sensor data of diverse animal species. Given the coexistence of generic and species-specific behavioural patterns among different species, we design a Shared-Preserved Convolution (SPConv) module. This module assigns an individual low-rank convolutional layer to each species for extracting species-specific features and employs a shared full-rank convolutional layer to learn generic features, enabling the CKSP framework to learn inter-species complementarity and alleviating data limitations via increasing data diversity. Considering the training conflict arising from discrepancies in data distributions among species, we devise a Species-specific Batch Normalization (SBN) module, that involves multiple BN layers to separately fit the distributions of different species. To validate CKSP's effectiveness, experiments are performed on three public datasets from horses, sheep, and cattle, respectively. The results show that our approach remarkably boosts the classification performance compared to the baseline method (one-for-one framework) solely trained on individual-species data, with increments of 6.04%, 2.06%, and 3.66% in accuracy, and 10.33%, 3.67%, and 7.90% in F1-score for the horse, sheep, and cattle datasets, respectively. This proves the promising capabilities of our method in leveraging multi-species data to augment classification performance.