If I put the high alert token on my home system. Does the token need to move with a fleet in order to convey the +1 movement?

I am thinking if you take warfare II first round and have 2 carrier with 1 movement on your home base, you can send each of the carriers to separate hexes 2 hexes away. Would the high alert token grant the +1 movement to the 2 separate fleets if it remains in the starting hex? Or does the token need to move with the fleet to grant the bonus to move?

High Alert grants + 1 movement to all fleets located in that hex until you move the High Alert out.

So generally, you do not move the High Alert until your last fleet is moved.

Some players leave the High Alert behind because it also gives +1 to hit in the hex it is in. That is a good boost to your space dock's defending fleet.

The FAQ has this to say on the subject:

"Q: With the Warfare II High alert token, do ships which start in the system of the token, but do not move with the token, get the +1 movement bonus?

A: Yes. At the start of an activation, all ships in a system with the high alert token gain +1 movement for that activation. This bonus is regardless of whether or not you decide to move the token with the ships."