Sedum mexicanum (Britton): A semi-hardy ground cover, likely from China, not Mexico. It is a lime green, upright variety that likes a bit more shade and water than most Sedum. It produces bright yellow flowers and makes an excellent choice for ground cover, retaining walls, and rock gardens.
Sedum are easy, resilient plants that thrive outdoors with full sun and great drainage. Plant in raised beds or containers with drainage holes and mix 50% coarse sand, pumice, or perlite into the soil to prevent rot. Regular water will help young plants establish roots and spread quickly, but mature Sedum can tolerate several months of drought. If you choose to propagate by hand, cut off the top 2.0"+ of stem and transplant it to re-root.