I am not assuming that one of the twins is stationary, but that one is moving with a different speed than the other. But this situation is symmetric, when A is moving away from B, then also B is moving away from A. Both can make the calculation of their ages and A comes to the conclusion that B will be younger, then B will make the calculation and to him A should be younger.
When the twin wants to return then his speed changes to -v. Then we cannot make a new calculation because their origins of their reference frames are not in the same place.
Einstein is assuming that the reference frame can change its speed or direction and the Lorentz transformation still can be used. Which is true it can or cannot?