Oblique Moves and Groups

I have a line of FP in a group. Groups are not permitted to move obliquely, so I would have to move each FP unit individually. After the moves, the FP are in a line again, as if a group move would have been done in the first place.

I realize that since I separated the FP units, they would not constitute a group during their activation. The question is, assume the opponent wins the next initiative and charges my FP units. Can I react as a group now, being that another command has been activated?

once you have completed the move you are again a Group. So if charged you perform as a Group.
In most cases there is not a difference in moving one unit at time, like probably in this case, in some other yes. For example you want to take a second move with that Group you cannot as you activated the single Units one by one.
So, in short, once you have COMPLETED the activation you are still a Group.