The paper is inspired by the paper [D. Buhagiar and E. Chetcuti, “On isomorphisms of inner product spaces”, Math. Slovaca 54, 109–117 (2004; Zbl 1065.03047)], showing that if \(V_1\) and \(V_2\) are two separable, real inner product spaces such that the modular ortholattices of their systems of finite/cofinite subspaces are algebraically isomorphic, then \(V_1\) and \(V_2\) are isomorphic inner product spaces. This result is here extended to real, complex or quaternionic inner product spaces that are not necessarily separable.