What is the mechanism for activity at the heliosheath to be transmitted back through the solar wind (swimming upstream as it were) to the Sun?
What do you propose would be the signs of this transmission of force? How much energy are you proposing is transmitted back to the Sun in order to create this effect?
Is there an analogous effect you can demonstrate with another fluid flow (such as water flowing down a radial surface, into a larger fairly static or dynamic pool, creating a shock region where the fast outward water flow hits the more static surrounding water). How would the action of fluids at the interface be transmitted back up the flow and have an effect on the water outlet?