It would future-proof and support the robustness of having several topic-focused groups, if admins can move posts and comment threads around, in order to keep discussions on topic.

So, apart from picking a new category, also i suggest having the option to move a post to a different group.

Use case:

I am developing a new setup for the Groups on the new membership site experience and would like transfer a large number (into the hundreds) existing posts and comment threads from one general group that's been serving my members well for some time now, into a number of new, more topic-focused groups that will be the future setup.