We report an analysis of time variations of several Voyager 1 Low Energy Charged Particle (LECP) rate channels for 2004 mostly in the pre-termination shock (TS) region and for 2005 in the heliosheath. Protons and oxygen ions coming from the TS during 2004 show autocorrelation peaks at approximately and full solar rotation period. We explain the apparent solar control of particle acceleration at the TS by invoking shock drift acceleration (SDA) which depends strongly on the angle Θ_Bn that the interplanetary magnetic field (IMF) makes with the shock surface. Preferred regions of acceleration occur where Θ_Bn is near 90°. IMF connection of Voyager 1 to preferred regions on the TS can enhance the access of accelerated particles. This geometrical situation is only available during 2004. Analyses of the data from 2003 and 2005 do not show peaks at or full solar rotation period.