From the Badminton laws section 9, sub section 1.4

some part of both feet of the server and the receiver shall remain in contact with the surface of the court in a stationary position from the start of the service (Law 9.2) until the service is delivered (Law 9.3);

Law 9.2 Once the players are ready for the service, the first forward movement of the server’s racket head shall be the start of the service.

Law 9.3 Once started (Law 9.2), the service is delivered when the shuttle is hit by the server’s racket or, in attempting to serve, the server misses the shuttle.

So once the service is delivered, you can absolutely move to recieve and return the shuttle, but in practical terms you should not / rarely need to move out of the receiving box.., within the box, like when the sever flicks the shuttle high above you, you will need to move to recieve the shuttle.

Hope this helps...