First stop treating reconnect as a fresh check. It means you've regained a view of something whose history may be incomplete. The person commissioning this interface needs to say which evidence identifies the retained completion and what happens when that evidence is absent.
Right, the same fixture job can run again. Don't attach a retained high to the latest selection just because the names match. Your review needs an agreed identity and lifecycle on both sides, with unmatched state left for reconciliation.
For the offline check, replay the same identified completion twice, then reconnect to it. Also present an old completion during a newer attempt and a completion without usable identity. Those are different cases; making every reconnect disappear would lose a real result that arrived while disconnected.