With version 2.4.5 from 30.09.20, Telegram introduced Anonymous Groups. This feature allows group admins to remain anonymous, as the name suggests - they post on behalf of the group and stay hidden from the list of members.
When connecting a group, TGmembership needs to verify whether the person who adds him has enough rights to do so. With groups that don't use the "anonymous admins" feature, the process is quite straightforward - you add the bot to your group, it does the rest.
It's a bit tricky when the "anonymous admins" feature is enabled. The procedure is the same as when you add a channel - forward any message sent on behalf of the group to the bot, and then to add him just as you would usually do.
Connect your group
Add the bot to your group
Grant admin rights
That's all. The bot is now ready to automate your business.