Yeah, I would like to suggest that the part of the flower stalk that had flowers be kept in a plastic bag (zip lock) or for me I put them in small plastic containers. I would shake them from time to time to see if there are seeds. When you see very small black seeds (they look very small though) then you sow them as edmund mentioned, separately in a container that you can put a lid on.
One thing I have learned is that you don't want your container with seeds to be rained on, too many things will happen, either seeds will be buried deep, or might get washed away or might bunch together, etc.
When you sow the seeds, just sprinkle them over the medium, you don't need to bury them at all.
Again do understand they are considered annuals, so if your mother plants does die, it's just their life cycle, grow some more with your seeds.
TTFN
Arvin