Next Point-of-Interest (POI) recommendation plays a vital role in human mobility prediction within Location-based Social Networks (LSBN), assisting individuals to decide on their next destination. However, traditional centralized systems rely on large datasets of previous POI check-ins, which raises privacy and computation concerns. In this regard, Federated Learning (FL) has emerged as a promising solution, enabling distributed training of machine learning models while preserving user privacy. In this paper, we propose a novel FL-based POI recommendation system, FedDist-POIRec, that utilizes Federated Distillation (FD) in a semi-synchronous framework to promote privacy, recommendation efficiency, and cope with resource heterogeneity by considering heterogeneous model architectures among users. Additionally, to alleviate the sparsity of user checkin lists, we employ a innovative knowledge aggregation technique, where the knowledge of each user is aggregated with that of users who share similar preferences. Simulation results demonstrate that FedDist-POIRec outperforms the baseline methods in terms of recommendation efficiency and communication cost, while keeping the computation cost at an acceptable level.