This sounds like a https://docs.moodle.org/27/en/Moodle_migration, a migration within the same server. Otherwise the general (not Softaculous) procedure would be https://docs.moodle.org/27/en/Site_backup and then https://docs.moodle.org/27/en/Site_restore.
Installing and upgrading help
Upgrade to 2.8.7+ partially worked
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