Did you mention the name of the internet source? I would be curious to see how it was advertised at the time you made the purchase.
Many parts of several types of ginger plants are edible; leaves, shoots, roots/rhizomes, etc. but you need to know the botanical name to be sure; the term 'edible ginger' may be a bit vague but not necessarily untrue. Some people just make the assumption that 'edible ginger' is the grocery store ginger root.
Yes, please, I would like to take you up on your offer to share a division. I would gladly send you a division of my plant in exchange or will send postage, whichever you prefer. Please send me a Tree-mail when you have time.
Thanks and good luck identifying your plant.
