When does a charge receive the reaction force? There is a charge $A$. If a charge $B$ suddenly appears, the electric field by $B$ propagates at the speed of light from $B$ to $A$. When it reaches $A$, $A$ receives a power.
Then, according to the law of action and reaction, $B$ receives the reaction of this action, but when?
 A: First it should be noted that your example violates charge conservation. Maxwells equations can not be applied to such a case. To answer the question behind the question. I will reformulate the question in an equivalent manner. 
Suppose a light source at rest emits two identical photons in opposite directions. Each photon carries off momentum but the recoil momenta cancel so there is no net reaction force. One of the photons gets absorbed by a distant receptor so the momentum of the receptor changes and is subject to a force. The reaction force is constituted by the disappearance of the photon momemtum.
A: As indicated in the previous answer, this situation violates charge conservation, so consider this problem instead:
You have two charges $A$ and $B$ held in position and separated by some distance $d$, and nothing is in between. Suppose you start jiggling $A$. This causes acceleration of a charge and so some energy will be radiated as an electromagnetic wave (it will feel like there is something resisting you while you shake the particle, hence you are doing work and this work is translated to energy and momentum in the EM wave. Also note that this isn't because of the field created by $B$).
After time $t=d/c$ the disturbance will reach $B$ which will jiggle in response to the subtle changes in the EM field, radiating energy in the process as well. The wave emitted by $B$ takes the same time $t$ to travel back to $A$.
Getting back to your question, by the same token, you may assume that it takes time $2t$ for $B$ to receive the reaction.
Strictly speaking, this is not a typical Newton action-reaction pair, since there is a time gap that the effect took to travel. Generally, Newton's third law is not applicable to electrodynamics since mechanical momentum is not always conserved. This can be visualized easily by taking two charges traveling perpendicularly. You will find that while the electric forces behave as you might expect, the magnetic forces felt by the two bodies is equal in magnitude but not opposite in direction (in fact, they will be perpendicular). 
