Using the insights we considered in the hint, we could cut from A to B. The other cut would be at right angles to the first and should touch one end of the first cut. That means making a line with B as its center. This line will intersect the edges of the cross at their midpoints.

We don’t need to have tremendous jigsaw skills to rearrange the four pieces into a square. Move the yellow piece to the other side of the green piece (point B to point A). Move the red piece to the other side of the blue piece (point B to point A again). Then move the yellow and green pieces together to the other side of the blue and red pieces.

Alternate solution:
If an asymmetric solution offends your sensibilities, use some of the same principles to make two cuts through the center of the cross. The cuts are made at the same angles as our previous solution.