If I interpret OP correctly: It's not the spambots that are the problem. It's Facebook that's the problem.

Then your mods are terrible. FB's moderation tools are primitive, but they do exist. Your group should require a moderator's approval to gain posting privileges, and require a few questions to be answered as well:

- Do you agree not to make posts advertising any business or profit-making entity on this group?

- Do you agree that all of your posts and comments on this group will be individually written by you?

Reject any user who doesn't say yes to both of those and set all new users to post approval for the first week.

It's a lot of work because, as mentioned, FB's tools are crap.

Your problem might be exacerbated by the subject matter.