Adding a supergroup to InviteMember is very similar to adding a channel.

Click Telegram Group:

Promote @InviteMemberBot to supergroup admins. It only requires one permission — Restrict Users (or Ban Users):

You might also need to change Who can add members setting to Only admins:

Now you can post a message in the group and mention @InviteMemberBot. 

Now go back to @InviteMember, you will see a confirmation:

Done!

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