I thought if i went up to him after collecting the artifact, the next part of the mission would kick in.... but it hasn't
Yes, once you have the artifact he's seeking, you simply need to talk to him to progress the quest.
If you can't talk to him (he's not highlighted as you approach the shop), you've got an issue.
Are you sure you've got the right artifact? You need a specific one:
If you've got this artifact and you've progressed the quest to the point where Kannik asks for it, you may have encountered a bug.