Federated recommendations (FRs), facilitating multiple local clients to collectively learn a global model without disclosing user private data, have emerged as a prevalent architecture for privacy-preserving recommendations. In conventional FRs, a dominant paradigm is to utilize discrete identities to represent users/clients and items, which are subsequently mapped to domain-specific embeddings to participate in model training. Despite considerable performance, we reveal three inherent limitations that can not be ignored in federated settings, i.e., non-transferability across domains, unavailability in cold-start settings, and potential privacy violations during federated training. To this end, we propose a transferable federated recommendation model with universal textual representations, TransFR, which delicately incorporates the general capabilities empowered by pre-trained language models and the personalized abilities by fine-tuning local private data. Specifically, it first learns domain-agnostic representations of items by exploiting pre-trained models with public textual corpora. To tailor for federated recommendation, we further introduce an efficient federated fine-tuning and a local training mechanism. This facilitates personalized local heads for each client by utilizing their private behavior data. By incorporating pre-training and fine-tuning within FRs, it greatly improves the adaptation efficiency transferring to a new domain and the generalization capacity to address cold-start issues. Through extensive experiments on several datasets, we demonstrate that our TransFR model surpasses several state-of-the-art FRs in terms of accuracy, transferability, and privacy.