Arcadelt covered it well. The book arts worker in me wants to recommend PVA adhesive instead of superglue, because PVA is archival - acid neutral and quite strong. However, my guess is the box probably wasn't constructed with PVA adhesive, so it would be one strong point in box that's going to decay otherwise regardless. Either way, practice applying the glue with a pin or tiny brush on a different, throwaway box first.
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