Any procedure to upgrade Joomla 2.5.28 to Joomla 3.5 with CiviCRM 4.4.4?
The first issue to raise is that CiviCRM 4.4 is not necessarily compatible with Joomla 3.5 according to this post: https://civicrm.org/blog/colemanw/announcing-civicrm-445  Since CiviCRM 4.6 apparently is compatible with Joomla 2.5, I suggest upgrading Civi first from 4.4 to 4.6.  Most CiviCRM documentation has to do with upgrading CiviCRM, rather than upgrading Joomla, so I'm not prepared to give advice on Joomla upgrades specifically.