I'm not a specialist of Lorentz transformation. I would like to know if the Lorentz transformation from one observer to another preserves the space distance between these two observers.

Example (edited): Two spaceships are flying through space at arbitrary, different velocities. Two signal flashes are shot simultaneously (Earth frame) from Earth to the spaceships, which are equidistant to Earth (Earth frame) at the moment of the simultaneous (Earth frame) two explosions at the arrival of the two flashes. Each space ship is measuring the space distance between the two flashes. Will their result be the same? And, will a measurement from Earth have a different result because of the length contraction effect? (No gravity must be taken into account. In case of need you may replace Earth by a third spaceship).