We have created a Linnworks / Zendesk integration which does exactly this. Its currently in the final stages of development and we anticipate being ready to launch before xmas. We are currently running a beta testing program. If you are interested in joining please email us at firstname.lastname@example.org.
You can see a thread explaining a bit more about what oFlow does, here: https://help.linnworks.com/support/discussions/topics/7000007370
Do you still want to connect Zendesk to Linnworks? oFlow.io has now launched!
oFlow is a customer service support tool that links your Linnworks database to your help desk, gathering customer and order history to view direct in the ticket.
If you are interested to try this feature and see how it can speed up your day, head over to our site. We have a free 30 day trial and no credit card required.
Any other questions, do let me know.