The phrase "also allowed to move" is correct and usable in written English.
It can be used in contexts where you want to indicate that someone or something has permission to move in addition to other actions or permissions.
Example: "In this game, players are also allowed to move after they make their initial choice."
Alternatives: "permitted to move as well" or "granted the ability to move".
The rabbis were also allowed to move on to new employment without ever being held accountable.
The Kanaks were then also allowed to move out of their reserve areas.
It's a process that wrestles with two competing philosophies around the idea of justice: justice for victims who have the right to be paid for their losses -- even when the offender spends time in jail -- and justice for juvenile offenders, who need to be held accountable but also allowed to move on from their crimes, and from the system.
To detect small overlaps between fragments, the correlated fragments were also allowed to move with respect to each other.
It was also allowed to move freely in the frontal plane.
It was kept alone in a terrarium, but was also allowed to move freely outside the cage in the flat.
To actually feel the amount of energy generated in your body is incredible, and oddly relaxing (you're also not allowed to move, so that certainly helped).
Use the elbow as a pivot point; it should not move so much up and down, but also should be allowed to move slightly forward in the follow-through.
We also demonstrate that the phase difference between the two frequencies controls not only the direction of motion but also which particles are allowed to move within a polydisperse mixture.
It also allowed Anthony to move to power forward, where he could use his quickness to great effect against bigger, slower defenders.
Free agency was supposed to not only make him the richest player ever, but also allowed him to move to New York, where his star would shine brighter than ever.
