I'm trying to figure out how a friend of mine add himself back in a chat group on telegram. How is that possible? I think he uses an app for that.
He can add himself only if he leaves and is not kicked out. If he gets kicked out, he won't be able to add himself back.
You will have to use the web version of telegram to exploit it. After logging in to the web.telegram.org website, select the group that you left from the left (direction) pane.
Now click on the group name from the top bar. In the dialog box that open, click 'Return to Group'! Hope the telegram developers market it as a feature for adding yourself back and accessing archives of groups that you used to be a part of.
A "mutual contact" can invite someone back into a group. The mutual contact needs to have your friend saved as a contact and your friend needs to have the mutual contact saved as a contact.
if a person left a group, only a mutual contact can bring him back (both need to know each other's phone numbers)— Telegram Messenger (@telegram) April 11, 2015