Once a sprint is marked as completed in Align, you can't make changes to it. But if you have the appropriate Team Role, can you reopen the sprint, add the stories, then complete the sprint again.
Once you correct your synch issue (and there's a lot of great troubleshooting information here: https://community.atlassian.com/t5/Jira-Align-articles/Jira-Align-and-Jira-Integration-Best-Practices-and-FAQ-Table-of/ba-p/1253497 ) you can go into iteration screen and unlock it.
Then you go to the Story backlog in Align and look at the sprint in question and the unassigned backlog together. Then just add the items from the unassigned backlog into the sprint.
You'll get a warning message because you're changing the scope of a sprint that's completed, but if you're trying to clean things up, that's OK. (And this is something that teams frequently have to do when they bring they're data into Algin and get the visibility into the complete structure and realize they haven't been updating status as they move along. We call this the "cleaning your room" stage.)
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