Padlet projects can be shared with groups via email or username.
Step 1: Once you created your wall, share this wall with your group members. Click on Modify This Wall and select Privacy. Add group member emails or usernames in the appropriate section and give them the ability to Write. Check that the Visibility is set to Private (only people that have been added can view/edit the Padlet).
Step 2: After adding group member emails, share your Padlet wall with your group by sending the link to them.