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May I know if there is any speedy way that our Unit leader can sign back all the missing Initial Unit Leader Signature on different merit badges for a group of scouts in the same MB or a different MBs for the same scout?
Yes. Use the Feature Assistant Extension Quick Entry to Add Merit Badges.
While you are not “adding” a new badge in this case, the feature has the ability to add the Initial Unit Leader Signature date for existing badges, if not already set.
However, to use if for existing badges, be sure to have more than one Scout selected. If you only have one scout selected, the badges previously started are greyed out and cannot be selected.