Can forces from outside the observable universe be observed through a distant object? I recently saw a video on dark flow from PBS space time on youtube, and it said that the flow had to be a constant motion, and not accelerating, because the object likely that caused the flow using gravity was now outside our sphere of influence due to the expansion of the universe faster than the speed of light.
However, is it not possible to observe something accelerate due to gravity from outside the observable universe, if we observe a distant object that is still inside the observable universe of the thing causing the pull, and also inside ours?
In other words, in the following picture, is it possible for A to observe the gravitational acceleration of B, even if A is outside the sphere of influence of C? 

 A: It is certainly possible that you could theoretically detect the previous gravitational effect on B due to C, as you observe B. Just keep in mind you are observing an effect that caused B to do something (maybe its peculiar velocity), by the time B emitted the light you are now seeing. 
To measure peculiar velocities it is difficult at or near the observable universe radius because we have no way of measuring velocity at those ranges other than the cosmic redshift, so can't tell if any peculiar component or not. At those distances there is no distance measurement other than the redshifts. Of course, if some astrophysical way could be found, to better measure cosmological distances beyond the current limits of the distance ladder, you might then. But it would still be a difficult
thing to do as you'd have to measure the peculiar velocities, and with it the local gravitational fields, or the other objects which can also affect B's peculiar velocity. 
I have not seen a paper that has done a calculation to determine the limits of what you can find out. But I am guessing intuitively it gets more inaccurate pretty quickly, since we've not detected everything around inside our observable universe either. Also, the universe's expansion will also put limits of how far back in time B can tell us anything about C.
You can also check @Gerbil's reference on a 2 year old answer, but I think it tries to answer whether you can see C's more current effect on B, whereas more pseudo-static gravitational potentials seem to me more possible. 
