For solar cycle 22 the large-scale interplanetary disturbances produced by the intense solar activity of March/June 1991 had a long-term effect on the recovery of galactic cosmic rays throughout the heliosphere that persisted for almost 5 years. At 1 AU, the recovery of 13 MeV/nucleon anomalous cosmic ray oxygen (ACR O+) is much more rapid than that of 265 MeV/nucleon galactic cosmic ray helium (GCR He), consistent with previous observations in the distant heliosphere <McDonald et al., 2000> and strengthening the concept that the region of the heliosheath plays an important role in the modulation of galactic cosmic rays. A comparison of the time histories of GCR He and ACR O+ at 1 and 44 AU observations suggest the recovery moves from the distant heliosphere inward toward 1 AU for this particular phase of the heliomagnetic cycle. There is a very low relative modulation potential, Φ, between 1 and 70 AU of 116 ¿ 6 MV for GCR He at solar minimum using the force field approximation. When combined with the small radial intensity gradients in the distant heliosphere, a much lower modulation potential is implied between 1 AU and the termination shock at solar minimum than had been assumed previously. There is no effect on the 13 MeV/nucleon ACR O+ intensity as the inclination of the heliospheric neutral current sheet decreases from 32¿ to its minimum value of 8¿.