If A accelerates, she can measure this acceleration, thus, she knows she is moving; although there is nothing relative to which she can be said to be moving. This begins to look like “absolute” motion; but can have little, or no, real meaning.
You have put your finger on the nub of newtonian mechanics. Quite simply, motion is a change in position vector, but in the absence of an origin for that vector, there is no way that a body can "know" it is moving at a constant speed. Beware of getting philosophical and introducing terms like "real meaning" - it can poison your physics!