Adding Security groups in SharePoint and Office 365 groups

Had the same trouble - but found solution for Adding Local AD Security Groups to SharePoint Online Groups - Synced to Azure AD via Azure AD Connect to ur O365 tenant

Connect-PnPOnline –Url https://site.sharepoint.com/sites/YourSite –Credentials $cred
Add-PnPUserToGroup -LoginName Local_AD_Security-Group -Identity 'YourSite Members'

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Should remember that the Site Group associated with your Share Point site i.e. The Office 365 group - cannot currently have a Security Group of users from a Local AD Group added to it - HOWEVER there are Scripts available to Sync the users from an Local AD Group to an Office 365 Group.

You will want users in the Office 365 Group as well so that they can be affiliated with your Microsoft Teams Team and Channels (If you use Microsoft Teams that is)

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Hope this helps someone.

Cheers,