I have uploaded the Installation Guides to both the ALM 12.53 & ALM 12.55 versions for your review.
As far as test cases & defects are concerned, these would only be affected if the database schema were changed between 12.2 & 12.5 which I don't think it was but if it were those changes are done automatically in the upgrade process.
Please review the chapters concerning upgrading projects. Recommendations are always that projects be backed up before running Verify and Repair on them.
So, I think if you follow the Installation Guide for whichever version you upgrade to, you should have no issues.[link text][1]
You should install/upgrade HP-sync to the latest version 12.53 SP2, then you need to REMOVE the HP-JIRA Adapter since it conflicts with ours.
THEN you can install their existing Orasi JIRAB 7.x.x adapter files back into their HP-Sync installation.
This works with QC11 - 12.53 (any QC patch)

There is no 12.55 version of Synchronizer yet, but should be out soon - a good reason NOT to go that far with QC version just yet.

We need to know what the JIRA Version is - this is on the Login screen for JIRA at the bottom of the page - you may has JIRA 7.x.x
7.x.x means any .x.x versions as long as the first number is still 7.

You also need to know if it is ''hosted'' by Atlassian or installed ''locally'' by the customer somewhere.

Since the Orasi adapter has a ''plugin'' that needs to be installed on the JIRA server, most ''hosted'' installations do not allow installing 3rd party plugins, so the Orasi Adapter will not work with the Atlassian ''Cloud'' (hosted) version, for instance.
Also, I uploaded a document that shows how to remove the standard HPE JIRA adapter which will need to be done[link text][2]

[1]: /storage/temp/706-alm-1255-install-windows.pdf
[2]: /storage/temp/707-how-to-remove-the-standard-hp-jira-adapter-from-sy.pdf