Advanced recommender systems usually involve multiple domains (scenarios or categories) for various marketing strategies, and users interact with them to satisfy their diverse demands. The goal of multi-domain recommendation is to improve the recommendation performance of all domains simultaneously. Conventional graph neural network based methods usually deal with each domain separately, or train a shared model for serving all domains. The former fails to leverage users' cross-domain behaviors, making the behavior sparseness issue a great obstacle. The latter learns shared user representation with respect to all domains, which neglects users' domain-specific preferences. These shortcomings greatly limit their performance in multi-domain recommendation. To tackle the limitations, an appropriate way is to learn from multi-domain user feedbacks and obtain separate user representations to characterize their domain-specific preferences. In this paper we propose $\mathsf{H^3Trans}$, a hierarchical hypergraph network based correlative preference transfer framework for multi-domain recommendation. $\mathsf{H^3Trans}$ represents multi-domain feedbacks into a unified graph to help preference transfer via taking full advantage of users' multi-domain behaviors. We incorporate two hyperedge-based modules, namely dynamic item transfer module (Hyper-I) and adaptive user aggregation module (Hyper-U). Hyper-I extracts correlative information from multi-domain user-item feedbacks for eliminating domain discrepancy of item representations. Hyper-U aggregates users' scattered preferences in multiple domains and further exploits the high-order (not only pair-wise) connections among them to learn user representations. Experimental results on both public datasets and large-scale production datasets verify the superiority of $\mathsf{H^3Trans}$ for multi-domain recommendation.