Place the colored shapes into the white area, without rotations or reflections, so that they fill it perfectly. The gray walls don't just block shapes, though - they act as portals!
When you place a shape, it has to stay in one piece, connected as it was before. However, cells separated by a gray wall are still connected - the shape stretches across the wall as if it had no thickness. The edge of the board also wraps around, so a piece that sticks off the right side reappears at the left, and so on.
This puzzle has only one solution. Good luck finding it!
Here are some examples of valid and invalid placements. This U-shaped piece can easily warp across a single gray wall:
This O-shaped shape can't be placed in the same way, since that would break it:
Adding another teleporter fixes this: