@... - Hey! In the end, my company decided not to integrate Instagram with Zendesk because it wasn't fit for purpose. Although I don't have any experience with the exact issue you mentioned, I thought I'd share some information about the integration for the whole community to see. When I asked Zendesk about the Instagram integration and how it works with Instagrams 'folders', I was told:

"The default behavior is that all [instagram] inboxes should come into Zendesk but there is no distinction in the messages when they do come in. The way to organize the messages is by manually moving them." (manually moving them in this case means = moving them from one view to another in Zendesk, not in the Instagram app...as you'll see below)

"Sorting/replies in the Instagram inbox will not be communicated/made available to Zendesk. If your team replies to a DM from the Instagram app itself, that reply will not show in the Zendesk ticket thread, and vice versa."