What should Pachauri have done? The answer's obvious: He should have left the @PMOIndia account untouched. He should have used Twitter's archiving tool to create a backup, for the records.
If the @PMOIndia account were to ever be lost, that archive could be used to make a PDF version, available online. Meanwhile, the @PMOIndia account itself would have been the archive, searchable via Twitter's advanced search, or by tools like Topsy.
No major harm has been done, except to the image of the PMO of the outgoing government. If access to @PMOIndiaArchive is being handed over to Team Modi, their first task will be to restore status quo: Delete the @PMOIndia account, and rename @PMOIndiaArchive back to @PMOIndia.