Why not invite them using the Invite mechanism?
It works smoothly. You can track the request. Resend it if necessary.
About inviting people to join your group:
Here's the Help page for using Invite.
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Take the time to edit your Invite Notice (in Admin, Settings, Notices) and use your toolbar to highlight your own content to personalize it. Save it for future use and activate it. Note that you can't remove what is there (the boilerplate) which is required at least in some jurisdictions. But by spaces, formats, bolding and italics, colour, you can get a pretty good invitation.
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Help available from Groups.io help and GMF wiki.
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