So you are looking to post to multiple Facebook Groups at the same time.
The first question is, are you trying to post to multiple Facebook Groups that you are the admin of, or are you trying to post to multiple Facebook Groups that you are only a member of?
Posting to multiple Facebook Groups at the same time that you have joined and are only a member
If you are trying to post to multiple Facebook Groups where you are NOT the admin, but are just a member, there is no Facebook-approved tool to do this.
Any tools that say they support this are violating Facebook’s terms of service, and will most likely result in your account getting temporarily or permanently banned.
I would recommend either posting manually in the Groups yourself, or highering a Virtual Assistant (VA) to do this for you.
Posting to multiple Facebook Groups at the same time that you are the Admin of
OneUp is a Facebook-approved social media scheduling tool that allows you to schedule posts to multiple Facebook Groups at the same time (in addition to Facebook Pages, and other social networks).
To use OneUp with a Facebook group, you MUST be one of the Group Admins. Facebook does not allow scheduling tools to post to Groups unless you are an admin.
Using OneUp, you can connect your Facebook Groups and Pages by clicking the Facebook Connect button.
Then you are ready to schedule a post.
First select which Facebook Group(s) or Page(s) you want to post to.
If you select a Facebook Group, you will see the option to either post to the Group as your personal profile, or post to the Group as your Facebook Page. (Note: Your Facebook Page must be an Admin of your Facebook Group to post as your Page to the Group)
Next, create your post.
You can set your post to publish once, or have it automatically repeat at whatever interval you choose.
You can also add images to the post if you want.
Once done, you can either post it now to your multiple Facebook Groups (and Facebook Pages), or schedule the post for the future.
You can try out OneUp for free.