Pharmaceutical-care services are increasingly transferred across jurisdictions through policy borrowing, professional expansion, implementation programmes, and adaptation of established community-pharmacy models. Yet a service that is effective in one setting cannot be assumed to remain operationally equivalent when introduced into a health system with different professional authority, workforce capacity, medicine availability, financing arrangements, information infrastructure, and patient expectations of pharmacists. This article develops a theory-building account of cross-border pharmaceutical-care transfer centered on the distinction between a service function and its local delivery form. A service function refers to the clinically or organizationally necessary work through which an intended medication-use purpose is achieved. Delivery form describes the personnel, workflow, regulatory permissions, payment arrangements, information channels, supply conditions, and encounter characteristics through which that work is carried out locally. Evidence from community-pharmacy implementation, workforce development, medicines shortages, prescribing policy, digital communication, care transitions, financing, and patient trust indicates that these conditions are analytically separable but operationally interdependent. Cross-border transfer should consequently be judged by whether locally adapted arrangements preserve the intended function under target-system conditions, rather than by visual or procedural similarity to the source service. The article advances functional equivalence as an evaluative principle for distinguishing acceptable adaptation from redesign that alters or compromises the intended service function. This approach shifts cross-country comparison away from intervention labels and broad cultural explanations toward explicit institutional, material, informational, and relational mechanisms that can be observed, tested, and modified.