Hi GT,
Hopefully my response below will not leave you as baffled as the actions of your client

Bear in mind that with respect to posting, Ledger is ultimately more concerned with the period/bucket number than the corresponding date/label of the bucket. If something posts to period/bucket 10 in FY2013 which happens to be labeled as June 2013, the info stays in that same bucket whether or not the "label" changes. The fact that one may change the label of bucket 1 in the FY2014 to say June 2013 will not cause the transactions posted to bucket 10 of FY2013 to move to bucket 1 of FY2014. If you've already posted the transactions to what would become the "wrong" bucket, then you'll have to unpost, re-label and then
re-post to the correct period number that now reflects the new labeling.
While changing the Fiscal Year in Adagio is entirely possible without importing transactions to a newly created GL, the mods needed to have accurate Financial Statements can be challenging. Special specs are usually required for the year of the change and another set of special specs for the first full year after the change. I've had some accountants\auditors want to look at the year of change as a "short" year while others a "long" year.
Best, Pete