The liquid-crystalline polymer system formed by solutions of hydroxypropylcellulose in water has a well known anomaly in the dependence of its mechanical complex modulus on its rheological history. After cessation of an initial rapid shear, the system evolves towards an 'equilibrium' state with a high modulus; after slow shear the 'equilibrium' state has a low modulus. Attempts to distinguish the two states by light scattering, birefringence or x-ray scattering have been unsuccessful. We present the first locally probing experiment, rheo-NMR, that sees a difference between these states. The results show clearly that the low-modulus state is ordered and evolves out of a state that has no macroscopic order (but may be ordered at the mesoscopic level) immediately after cessation of the shear. The high-modulus state is much less ordered, although it evolves from a rather well flow-aligned state immediately after cessation of the shear.