To associate an Intercom conversation to a Jira issue you will have to know the URL to the Intercom conversation that you would like to link.
Open Intercom, select the conversation in your Inbox and copy the URL from your browser's address bar.
Now, create a new Jira issue or open an existing one.
With the issue open, click on the Actions (•••) menu (1) on the top right of the issue view and select Link Intercom conversation (2).
In the modal dialog paste the conversation URL (1) into the input field, then click Submit (2).
Your conversation is now linked and you can find a Note with the issue reference posted to the Intercom conversation. To explore the linked conversation in the issue view, click on the Linked conversations issue glance (1) in the right-side column which will show all linked Intercom conversations. The badge on the issue glance (2) allows you to quickly see how many conversations the current issue has linked to it.
On the Jira issue view, click on the issue glance called Linked conversations (1) in the right-side column. This will open the issue glance and show all linked Intercom conversations.
Find the conversation that you would like to unlink, then click the more actions (•••) menu (1) for that conversation and select Unlink (2).
If your Jira project is a Jira Service Management (JSM) project and your Jira administrator has enabled conversation linking support, then Jira Service Management users with access to the request portal can link and unlink Intercom conversations with the JSM requests that they have access to.
In the request view, JSM users can link a conversation by clicking on the Link Intercom conversation button (1) and pasting an Intercom conversation URL as described in Creating a link.
Once there are one or more links associated with a request, the app will render a card for each linked Intercom conversations (2). Users can then open the linked conversation in Intercom (3) or unlink (4) it using the action links at the bottom of the card.