The best way is to not move it in the first place. There isn’t really any reason to move it away from where it was created. Leave it there and putting the hatching on it. Or, if you feel you absolutely have to move it, convert it to a component and move a copy of it away from the model and edit that copy.
Since you haven’t shared your SKP file or even an image, it’s difficult to tell you exactly how to put the group back where it belongs. If someone sent me a file with that problem, though, I would most likely delete the group and start over.
The Move tool is the thing to use to align just about anything with anything else. However, if you’re not up to speed on the use of the tool, and particularly with the use of inferencing to guide and control the move, you need to take a time out for an intensive study/practice session to get these skills under control, since being able to move and position things with speed and precision is absolutely essential.