This paper examines the Root solution of the Skorokhod embedding problem given full marginals on some compact time interval. Our results are obtained by limiting arguments based on the finitely many marginals Root solution of Cox, Oblaj, and Touzi [Probab. Theory Related Fields, 173 (2019), pp. 211-259]. Our main result provides a characterization of the corresponding potential function by means of a convenient parabolic PDE.