With the rapid proliferation of edge computing, Radio Frequency Fingerprint Identification (RFFI) has become increasingly important for secure device authentication. However, practical deployment of deep learning-based RFFI models is hindered by a critical challenge: their performance often degrades significantly when applied across receivers with different hardware characteristics due to distribution shifts introduced by receiver variation. To address this, we investigate the source-data-free cross-receiver RFFI (SCRFFI) problem, where a model pretrained on labeled signals from a source receiver must adapt to unlabeled signals from a target receiver, without access to any source-domain data during adaptation. We first formulate a novel constrained pseudo-labeling–based SCRFFI adaptation framework, and provide a theoretical analysis of its generalization performance. Our analysis highlights a key insight: the target-domain performance is highly sensitive to the quality of the pseudo-labels generated during adaptation. Motivated by this, we propose Momentum Soft pseudo-label Source Hypothesis Transfer (MS-SHOT), a new method for SCRFFI that incorporates momentum-center-guided soft pseudo-labeling and enforces global structural constraints to encourage confident and diverse predictions. Notably, MS-SHOT effectively addresses scenarios involving label shift or unknown, non-uniform class distributions in the target domain—a significant limitation of prior methods. Extensive experiments on real-world datasets demonstrate that MS-SHOT consistently outperforms existing approaches in both accuracy and robustness, offering a practical and scalable solution for source-data-free cross-receiver adaptation in RFFI.