Completing Into the Unkown

[pgfrix]

A player who plays through one or more of the quests receives a Chronicle sheet for Into the Unknown, noting which specific quests he played. He can later play the rest of the quests in the series, earning greater rewards (see the Variable Rewards boon on the Chronicle sheet at the end of this series). If the player created his own 1st-level character, he applies the Chronicle sheet to that character. If he instead used one of the 1st-level Starfinder Society pregenerated characters, he can apply the Chronicle sheet to a 1st-level Starfinder Society character. If that character gains XP from another Chronicle sheet, he can no longer earn additional rewards for that character for playing the other Into the Unknown quests.

This is an instance of aspirational design being slaughtered by their tech.  It's clear that the intent is exactly as described - go back and finish later if you're not done.

The reality is that once your PFS ID is reported on a specific character, the reporting will likely barf out that character number if it's reported again.  I suspect the most common solution to this problem is 'finishing players' simply won't be reported on their second table.  This becomes problematic if that ID is necessary to make a legal table minimum.

Take away - expect much strangeness, but yes, you should be able to finish the Quests at another table assuming all pertinent criteria align.