Longitudinal field μSR measurements in applied fields parallel and perpendicular to the c-axis of the hexagonal heavy-fermion antiferromagnet Ce(7)Ni(3) served to monitor the 4f-spin dynamics across the magnetic phase diagram in the B-T plane, which consists of an incommensurate/commensurate antiferromagnetic (AF) section below 1.9 K/0.7 K and below an applied field B of 0.25 T, and for B along the c-axis, of a field-induced magnetic (FIM) section for B≥0.6 T and below 0.5 K. The observed μ(+) spin-lattice relaxation rates reveal persisting spin dynamics across the whole phase diagram, reflect the various phase boundaries and are interpreted to arise in the AF and FIM phases from the Ce3 sublattice (the Ce ions are located on three different sublattices) and in the intermediate phase, viewed as a short range ordered (SRO) state, also from the Ce1 and Ce2 sublattices with slower fluctuation rates. In the paramagnetic regime the Ce1 sublattice displays the slowest spin dynamics. In the FIM phase the fraction of relaxing μ(+) appears to shrink with rising B, evidencing a possible phase separation.