Hootsuite used to allow us to share to many Facebook public groups do you recall? But terms of service and they had to stop I guess. Anyone know of any other automated services that allow you to share content to multiple Facebook groups you don't actually own?
Don't know any tool doing it, but I wouldn't use any if I were you mate. These tricky techniques never work.
You want to submit your content to multiple facebooks groups just in a single click, isn't it look spammy? Why do this? Sorry, I don't know about these type of tools and also recommended you to not to use this type of tools if there are any.