In the figure shown, the magnet is pushed towards the fixed ring along the axis of the ring and it passes through the ring.

When magnet goes towards the ring the face B becomes south pole and the face A becomes north pole

When magnet goes away from the ring the face A becomes north pole and the face B becomes south pole

When magnet goes away from the ring the face B becomes north pole and the face A becomes south pole

The face A will always be a north pole