Insert a shovel into the ground, 1 to 2 inches from the base of the plant. Gently dig under the Scotch moss until you have loosened the root system from the soil.
Lift the plant out of the soil, including the root system. Break the plant in half, gently teasing the roots apart. Replace 1/2 of the plant in the original hole. Fill the hole with soil and firm it with your hands.
Plant the second half of the plant in your desired location. The site should have well-draining soil and full to partial sun. You can divide the plants for propagation in fall or early spring.