Suzanne, if you want your amaryllis to focus on next year's blooms, you should remove the whole bloom stalk when the blooming period is over, leaving just the leaves. They can be propagated from seeds, but it is a multi-year project to get a bulb capable of flowering.
I always cut the stem back to the plant after the blooms fades.
I agree with Douglas. Cut off bloom stalk and plant in a semi-shady location. It will bloom in Apr/May next year.
I have found Amaryllis to be very hardy. I cut back the bloom stem. I even cut back the leaves when they become damaged or get in the way of other plants. The ones in full sun have more blooms than the ones in shaded area. In fact one of mine has been transplanted 4 times. It makes the loveliest of all fifteen or so amaryllis plants.
Just cut back the bloom stalk after it has flowered and dies . The green leaves should remain. Ours were in the ground and have split like crazy. I have taken the large bulbs and potted them for another garden and they continue to bloom each season. Very hardy. Ours are in both sun and shade and all are doing beautifully. Wish the flower stayed longer. Good luck
Do you keep it watered? Mine just bloomed-after 5 years of nothing.