Lorentz was the first to obtain the equations which relate the space and time coordinate of two frames of reference moving with a constant velocity with reference to each other and obeying the postulate of STR giving by Einstein, these equations are called Lorentz Transformation Equation.
Let us consider two observer O and O' in frame of references S and S'. The frame S' is moving with a uniform velocity v with reference to frame S, in + x direction. At time (t=0) observer O and O' are at the origin of the frame of reference S and S'.