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In this paper a novel representation of transfer functions of sampled-data systems in the lifted domain is proposed. The main idea is to express these transfer functions by the STPBC (systems with two-point boundary conditions) machinery avoiding the appeal to the state space in the lifted domain. This produces a compact LTI description of sampled-data systems in which the intersample dynamics are driven solely by the open-loop dynamics of continuous-time parts of the system and discrete-time dynamics shows up through a reshaping of the boundary conditions. The proposed representation simplifies manipulations over sampled-data systems and enables one to keep track of their structure under multi-level algebraic manipulations.