It's possible to reply to received Instagram messages from Agorapulse Inbox. First, you'll need to activate the Instagram Direct messages - here's how to do that.

After successful activation, new Instagram messages will be synced into Agorapulse Inbox in real-time. They can be filtered by Direct messages filter at the top.

At this moment, it's technically not possible to initiate / start new Instagram conversation with a user, from Agorapulse. It's only possible to reply to received messages.