I have a set of lines with different colors.
When I move these lines by "Translate" command to different locations
all the lines became white in Default) Color. Is there any way to keep the same color as Parent Lines
I don't think you can keep the same color in your situation, because when you use the translate feature, you are not actually moving your line, but you are creating a new feature that represents the old line in the new position, so new feature default color. You should modify the parent feature of the line (for example its starting point) to move it in the new position and keep the graphic properties.
Do you need to keep the history of the lines and the translate.
If not, turn history off (create datum)and use the no-keep option. This will translate your existing lines maintaining their graphic properties and not create new lines.