We present a combined magnetic neutron scattering and muon spin rotation study of the nature of the magnetic and superconducting phases in electronically phase separated La(2-x)Sr(x)CuO(4+y), x=0.04, 0.065, 0.09. For all samples, we find long-range modulated magnetic order below T(N) is approximately equal to Tc=39 K. In sharp contrast to oxygen-stoichiometric La(2-x)Sr(x)CuO(4), we find that the magnetic propagation vector as well as the ordered magnetic moment is independent of Sr content and consistent with that of the "striped" cuprates. Our study provides direct proof that superoxygenation in La(2-x)Sr(x)CuO(4+y) allows the spin stripe ordered phase to emerge and phase separate from superconducting regions with the hallmarks of optimally doped oxygen-stoichiometric La(2-x)Sr(x)CuO(4).