Your lilies are beautiful and my sympathies at the loss of your mother. From the image you sent it looks like you have the fragrant 'Stargazer' lilies. They seem very happy in their new location. You can snip off the blooms once they fade but leave the tall stem and leaves until they begin to turn yellow with the fall weather. The green leaves make food for next year's flowers. Once the foliage all turns yellow their job is done so cutting the tall stems to a few inches above the ground will help to prevent winter storms from rocking them about. In spring you will see new green shoots poking out of the soil and at that time I often will cut any remaining stem from last year off at ground level. Leaving a bit of stem over the winter helps to mark the lily patch so that I won't forget and try to plant something new on top of the lily bulbs lying dormant below ground. If you live in a very cold climate a mulch of wood chips or bark two inches deep will help to insulate the bulbs from a deep freeze. Keep growing, Marianne Binetti