One inbox, four channels. The agent experience is the same everywhere; delivery and a few rules differ per channel.
Agent replies are delivered live to the embedded webchat widget. The customer sees them appear in real time, with the agent's name, exactly as they'd see a bot message. When an agent opens the thread, the customer's bubbles get a Seen receipt. There's nothing extra to configure beyond embedding the widget.
If the widget is closed when an agent replies, its unread badge increments so the customer knows to reopen it.
Intercom is two-way. Replies sent from the inbox are posted to Intercom as the linked admin (see Linking Intercom admins), and actions taken inside Intercom are mirrored back into the inbox:
If Intercom assigns a conversation to someone who isn't a linked inbox agent, the inbox leaves the existing assignment alone rather than dropping it from your queue.
Replies are delivered to the customer's chat through your Telegram bot. There's no service window, so you can reply whenever the conversation is open. Connect Telegram via the Telegram deployment guide.
WhatsApp enforces a 24-hour customer-care window: you can send free-form replies only within 24 hours of the customer's most recent message. The composer tracks this for you: when the window is open you reply normally; when it closes it shows a banner and blocks free-form replies.
Replies are delivered to the customer's Messenger chat through your Facebook Page. Messenger has two windows rather than one, and the composer tells you which you are in.
For 24 hours after the customer's last message you reply normally. Between then and seven days, only a person may answer: the bot stops, an agent can still reply, and the composer says the reply goes as a human agent reply. Past seven days nothing can be sent and the composer stops you.
Replies are delivered to the customer's Instagram inbox, and the windows work exactly as they do on Messenger: free for 24 hours, a person only for seven days, nothing after that.
Replies to your stories and mentions in other people's arrive here as ordinary direct messages, but only once you have switched them on for that account. Until then they are not answered and do not reach the inbox at all. See the Instagram deployment guide.