A player activated a system and moved a large fleet into it, on the next movement phase the player forgot to move a ship in their previous turn, can you move a ship, into a system you activated on your last movement phase, or is it an all or nothing situation?

Look I'm fairly lenient, this isn't chess, within the next few minutes of them moving ships in that's ok, if it comes around to their turn again though, I'd say 'well you should've remembered that', but a few extra seconds to move things in, umming and are-ing that's ok.

Reason I wouldn't let them be too retroactive is, one day someone will do that with warfare, so they need to be on their toes ready to move everything they want to move, and also, if the system they're going after reinforced and now suddenly they want to move their destroyer in to attack newly made fighters, instead of or in conjunction with a carrier for example, we then have a problem.

I have to agree with Conza, if it's a friendly game and you're still moving stuff into a system that's fine - fly that baby in there. If everyone else has taken a turn, and you've realized that you messed up you can't then fly your ship into that system. It's position on the map may have influenced the turn of everyone else. Part of learning the game is knowing what to do with your stuff right now, to set yourself up for your next action/turn.

By the rules, no.

You can't activate the system again, so you can't move ships into it.