It is possible to transplant roses, but it should be done in early spring when the plant is still dormant.
Prepare a hole for the rose and fertilize, then carefully use a spade around the rose bush to be transplanted. Go wide around the plant and deep into the soil to avoid cutting any of the roots.
Gently remove the plant and move it to its new home. Do make sure the new location has at least 6 hours of sunlight a day.