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Open the Facebook app. Tap ☰. Tap Groups. Tap the group you want to invite people to. Tap Add Members. Enter the email of the person you want to invite. Tap Done.
If prompted, enter your username or password and tap Log in. This in the menu bar at the bottom of the screen.  If you are making a new group tap Create Group.  You can add multiple emails at once. An invitation to join the group will be sent to that person's email. They can click the link and login with their Facebook account to join the group. If creating a new group, this button will labeled Next.